Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #11763516 | C2 | semidirect |
| 2. #11763479 | C2 | semidirect |
| 3. #11763172 | C2 | semidirect |
| 4. #11763155 | C2 | semidirect |
| 5. #11763111 | C2 | semidirect |
| 6. #11763100 | C2 | semidirect |
| 7. #11763002 | C2 | semidirect |
| 8. #11762936 | C2 | semidirect |
| 9. #11762921 | C2 | semidirect |
| 10. C4×#63228 | C2 | semidirect |
| 11. C17×#459 | C2 | semidirect |
| 82. D4×C17 | #41 | semidirect |
| 131. #459 | D17 | semidirect |
| 170. C17 | #3366 | semidirect |
| 218. D4 | #63254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763516 | 2 |
| #11763479 | 2 |
| #11763172 | 2 |
| #11763155 | 2 |
| #11763111 | 2 |
| #11763100 | 2 |
| #11763002 | 2 |
| #11762936 | 2 |
| #11762921 | 2 |
| C4×#63228 | 2 |
| C17×#459 | 2 |
| #3366 | 17 |