Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11763524 | C2 | semidirect |
| 2. #11763464 | C2 | semidirect |
| 3. #11763207 | C2 | semidirect |
| 4. #11763132 | C2 | semidirect |
| 5. #11763126 | C2 | semidirect |
| 6. #11763099 | C2 | semidirect |
| 7. #11763089 | C2 | semidirect |
| 8. #11763059 | C2 | semidirect |
| 9. #11762888 | C2 | semidirect |
| 10. #11762850 | C2 | semidirect |
| 11. C4×D8×C17 | C2 | semidirect |
| 100. C8×C17 | #41 | semidirect |
| 130. C4×D8 | D17 | semidirect |
| 168. C17 | #3354 | semidirect |
| 229. C8 | #63252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763524 | 2 |
| #11763464 | 2 |
| #11763207 | 2 |
| #11763132 | 2 |
| #11763126 | 2 |
| #11763099 | 2 |
| #11763089 | 2 |
| #11763059 | 2 |
| #11762888 | 2 |
| #11762850 | 2 |
| C4×D8×C17 | 2 |
| #3354 | 17 |