Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
198 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #10587581 |
| commutator, cosocle | C42×C17 | C23 |
| Frattini | C42 | C22×D17 |
| Fitting | C17×#334 | C2 |
| socle | C22×C17 | #121 |
| hypercenter | #334 | D17 |
| hypocenter | C17 | #1687 |
| LCS | G ▷ C42×C17 ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #334 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11763186 | C2 | semidirect |
| 2. #11763005 | C2 | semidirect |
| 3. #11762888 | C2 | semidirect |
| 4. #11762552 | C2 | semidirect |
| 5. C17×#334 | C2 | semidirect |
| 49. C8×C17 | D8 | semidirect |
| 67. #334 | D17 | semidirect |
| 85. C17 | #1687 | semidirect |
| 119. C8 | D136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763186 | 2 |
| #11763005 | 2 |
| #11762888 | 2 |
| #11762552 | 2 |
| C17×#334 | 2 |
| #1687 | 17 |