Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11763532 | C2 | semidirect |
| 2. #11763519 | C2 | semidirect |
| 3. #11763164 | C2 | semidirect |
| 4. #11763160 | C2 | semidirect |
| 5. #11763117 | C2 | semidirect |
| 6. #11763100 | C2 | semidirect |
| 8. #11763015 | C2 | semidirect |
| 9. C4×#63219 | C2 | semidirect |
| 11. C8×Q8×C17 | C2 | semidirect |
| 124. C8×Q8 | D17 | semidirect |
| 161. C17 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763532 | 2 |
| #11763519 | 2 |
| #11763164 | 2 |
| #11763160 | 2 |
| #11763117 | 2 |
| #11763100 | 2 |
| #11763025 | 2 |
| #11763015 | 2 |
| C4×#63219 | 2 |
| C4×D136 | 2 |
| C8×Q8×C17 | 2 |
| #3360 | 17 |