Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
3422 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 3422 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting | C2×C17×#120 | C2 |
| hypercenter | C2×#120 | D17 |
| hypocenter | C17 | #2846 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×D17 | C2 | semidirect |
| 2. C2×#10587623 | C2 | semidirect |
| 3. #11762665 | C2 | semidirect |
| 4. #11762664 | C2 | semidirect |
| 5. C2×C17×#120 | C2 | semidirect |
| 10. C22×D4×C17 | C22 | semidirect |
| 11. C22×C22⋊D17 | C22 | semidirect |
| 13. C2×C22⋊C4×C17 | C22 | semidirect |
| 14. C2×C22⋊Dic17 | C22 | semidirect |
| 16. C2×#63227 | C22 | semidirect |
| 18. C24×C17 | D4 | semidirect |
| 20. C24×C17 | C23 | semidirect |
| 26. C23×D17 | D4 | semidirect |
| 30. C22×C4×C17 | C23 | semidirect |
| 32. C22×Dic17 | C23 | semidirect |
| 63. C22×C17 | #120 | semidirect |
| 69. C2×D17 | #120 | semidirect |
| 74. C2×#120 | D17 | semidirect |
| 87. C22×D4 | C2×D17 | semidirect |
| 92. C2×C22⋊C4 | C2×D17 | semidirect |
| 93. C17 | #2846 | semidirect |
| 102. C24 | C22⋊D17 | semidirect |
| 104. C24 | C22×D17 | semidirect |
| 109. C22×C4 | C22×D17 | semidirect |
| 143. C22 | #10587623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D17 | 2 |
| C2×#10587623 | 2 |
| #11762665 | 2 |
| #11762664 | 2 |
| C2×C17×#120 | 2 |
| #2846 | 17 |