Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
3666 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3666 conjugacy classes of subgroups — too many to draw. Only its 667 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D17 |
| commutator, cosocle | C23×C17 | C25 |
| Frattini | C23 | C24×D17 |
| Fitting | C2×C17×#383 | C2 |
| socle | C24×C17 | C24 |
| hypercenter | C2×#383 | D17 |
| hypocenter | C17 | C2×#2818 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C24 ◁ C2×#383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10587560 | C2 | semidirect |
| 2. C22×#10587562 | C2 | semidirect |
| 3. #14536827 | C2 | direct (N × H) |
| 4. C2×#11762727 | C2 | semidirect |
| 5. C2×#11762719 | C2 | semidirect |
| 6. C2×C17×#383 | C2 | semidirect |
| 10. C2×#10587560 | C22 | semidirect |
| 12. C2×#10587562 | C22 | semidirect |
| 16. #11762727 | C22 | semidirect |
| 17. #11762719 | C22 | semidirect |
| 19. C17×#383 | C22 | semidirect |
| 31. C2×C42×C17 | D4 | semidirect |
| 63. C42×C17 | C2×D4 | semidirect |
| 96. C2×#383 | D17 | semidirect |
| 123. #383 | C2×D17 | semidirect |
| 125. C2×C17 | #2818 | semidirect |
| 148. C2×C42 | D68 | semidirect |
| 151. C17 | C2×#2818 | semidirect |
| 176. C42 | C2×D68 | semidirect |
| 216. C2 | #14536827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587560 | 2 |
| C22×#10587562 | 2 |
| #14536827 | 2 |
| C2×#11762727 | 2 |
| C2×#11762719 | 2 |
| C2×C17×#383 | 2 |
| C2×#2818 | 17 |