Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
196 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#595 |
| commutator, socle | C2×C17 | C2×C4×C8 |
| Fitting | C17×M32 | C4 |
| prime radical | C22×D17 | C2×C8 |
| cosocle | C8×D17 | C23 |
| hypercenter | M32 | #595 |
| hypocenter | C17 | C4×M32 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C8 ◁ M32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11763696 | C2 | semidirect |
| 4. C16×#595 | C2 | semidirect |
| 9. #10587538 | C4 | semidirect |
| 14. #10587530 | C4 | semidirect |
| 16. C17×M32 | C4 | semidirect |
| 17. #10587483 | C4 | semidirect |
| 18. #10587469 | C4 | semidirect |
| 35. #63216 | C2×C4 | semidirect |
| 36. C16×C17 | C2×C4 | semidirect |
| 37. #63214 | C2×C4 | semidirect |
| 60. #595 | M32 | direct (N × H) |
| 81. M32 | #595 | direct (N × H) |
| 88. C17 | C4×M32 | semidirect |
| 106. C16 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763865 | 2 |
| C2×C8×#595 | 2 |
| #11763696 | 2 |
| C16×#595 | 2 |
| M32×D17 | 2 |
| C4×M32 | 17 |