Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763544 | C2 | semidirect |
| 2. #11763532 | C2 | semidirect |
| 3. #11763193 | C2 | semidirect |
| 4. #11763182 | C2 | semidirect |
| 5. #11763032 | C2 | semidirect |
| 6. #11763025 | C2 | semidirect |
| 7. #11763020 | C2 | semidirect |
| 9. C4×#63219 | C2 | semidirect |
| 10. C4×#63219 | C2 | semidirect |
| 11. C8×Q8×C17 | C2 | semidirect |
| 129. C8×Q8 | D17 | semidirect |
| 166. C17 | #3394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763544 | 2 |
| #11763532 | 2 |
| #11763193 | 2 |
| #11763182 | 2 |
| #11763032 | 2 |
| #11763025 | 2 |
| #11763020 | 2 |
| #11763005 | 2 |
| C4×#63219 | 2 |
| C8×Q8×C17 | 2 |
| #3394 | 17 |