Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#10587598 | C2 | semidirect |
| 2. #11763357 | C2 | semidirect |
| 3. C4×#63254 | C2 | semidirect |
| 4. #11763030 | C2 | semidirect |
| 5. #11763022 | C2 | semidirect |
| 6. #11763020 | C2 | semidirect |
| 7. #11763014 | C2 | semidirect |
| 8. #11763006 | C2 | semidirect |
| 9. C4⋊C8×D17 | C2 | semidirect |
| 10. #11762802 | C2 | semidirect |
| 11. C17×#459 | C2 | semidirect |
| 57. #63254 | D4 | semidirect |
| 136. C4×C17 | #135 | semidirect |
| 153. #459 | D17 | semidirect |
| 194. C17 | #3035 | semidirect |
| 292. C4 | #10587598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587598 | 2 |
| #11763357 | 2 |
| C4×#63254 | 2 |
| #11763030 | 2 |
| #11763022 | 2 |
| #11763020 | 2 |
| #11763014 | 2 |
| #11763006 | 2 |
| C4⋊C8×D17 | 2 |
| #11762802 | 2 |
| C17×#459 | 2 |
| #3035 | 17 |