Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11763360 | C2 | semidirect |
| 2. C4×#63254 | C2 | semidirect |
| 3. #11763135 | C2 | semidirect |
| 4. #11763101 | C2 | semidirect |
| 5. #11763010 | C2 | semidirect |
| 6. #11763004 | C2 | semidirect |
| 7. #11762955 | C2 | semidirect |
| 8. #11762896 | C2 | semidirect |
| 9. #11762889 | C2 | semidirect |
| 10. #11762861 | C2 | semidirect |
| 11. C17×#476 | C2 | semidirect |
| 88. D4×C17 | #41 | semidirect |
| 114. Dic34 | #41 | semidirect |
| 143. #476 | D17 | semidirect |
| 187. C17 | #3106 | semidirect |
| 241. D4 | #63256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763360 | 2 |
| C4×#63254 | 2 |
| #11763135 | 2 |
| #11763101 | 2 |
| #11763010 | 2 |
| #11763004 | 2 |
| #11762955 | 2 |
| #11762896 | 2 |
| #11762889 | 2 |
| #11762861 | 2 |
| C17×#476 | 2 |
| #3106 | 17 |