Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
13646 conjugacy classes of subgroups; only the 1539 normal subgroups are shown.
This group has 13646 conjugacy classes of subgroups — too many to draw. Only its 1539 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C25 | C22×D17 |
| commutator, cosocle | C23×C17 | C25 |
| Frattini | C23 | C24×D17 |
| Fitting | C22×C17×#95 | C2 |
| socle | C25×C17 | C23 |
| hypercenter | C22×#95 | D17 |
| hypocenter | C17 | C22×#392 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C25 ◁ C22×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×D68 | C2 | semidirect |
| 2. C23×#63227 | C2 | semidirect |
| 3. C2×#11762719 | C2 | direct (N × H) |
| 4. C22×C17×#95 | C2 | semidirect |
| 8. C23×D68 | C22 | semidirect |
| 11. C22×#63227 | C22 | semidirect |
| 12. #11762719 | C22 | direct (N × H) |
| 14. C2×C17×#95 | C22 | semidirect |
| 20. C24×D17 | D4 | semidirect |
| 23. C23×C4×C17 | D4 | semidirect |
| 30. C22×D68 | C23 | semidirect |
| 32. C2×#63227 | C23 | semidirect |
| 33. C17×#95 | C23 | semidirect |
| 47. C23×D17 | C2×D4 | semidirect |
| 51. C22×C4×C17 | C2×D4 | semidirect |
| 78. C22×D17 | C22×D4 | semidirect |
| 81. C2×C4×C17 | C22×D4 | semidirect |
| 88. C22×#95 | D17 | semidirect |
| 89. C22×C17 | #392 | semidirect |
| 113. C2×#95 | C2×D17 | semidirect |
| 114. C2×C17 | C2×#392 | semidirect |
| 133. C23×C4 | D68 | semidirect |
| 137. #95 | C22×D17 | semidirect |
| 138. C17 | C22×#392 | semidirect |
| 162. C22×C4 | C2×D68 | semidirect |
| 188. C2×C4 | C22×D68 | semidirect |
| 195. C22 | #11762719 | direct (N × H) |
| 205. C2 | C2×#11762719 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D68 | 2 |
| C23×#63227 | 2 |
| C2×#11762719 | 2 |
| C22×C17×#95 | 2 |
| C22×#392 | 17 |