Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
752 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 246 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 | C22×#595 |
| commutator | C2×C17 | C43 |
| Fitting | C17×#95 | C4 |
| socle | C23×C17 | C22×C4 |
| prime radical, cosocle | C23×D17 | C23 |
| hypercenter | #95 | #595 |
| hypocenter | C17 | C4×#95 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C2×C4×#595 | C4 | semidirect |
| 9. (C2×#595)⋊C4 | C4 | semidirect |
| 10. C17×#95 | C4 | semidirect |
| 11. #10587502 | C4 | semidirect |
| 40. C2×#595 | C42 | semidirect |
| 44. C2×C4×C17 | C42 | semidirect |
| 46. C2×Dic17 | C42 | semidirect |
| 64. #595 | #95 | direct (N × H) |
| 84. #95 | #595 | direct (N × H) |
| 85. C17 | C4×#95 | semidirect |
| 123. C2×C4 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#595 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| #95×D17 | 2 |
| C4×#95 | 17 |