Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10587590 | C2 | semidirect |
| 2. #11763480 | C2 | semidirect |
| 3. #11763464 | C2 | semidirect |
| 4. #11763182 | C2 | semidirect |
| 5. #11763038 | C2 | semidirect |
| 6. #11763020 | C2 | semidirect |
| 7. #11763005 | C2 | semidirect |
| 8. #11762973 | C2 | semidirect |
| 9. #11762956 | C2 | semidirect |
| 10. C4×#63219 | C2 | semidirect |
| 11. C8×D4×C17 | C2 | semidirect |
| 81. #63219 | D4 | semidirect |
| 128. C4×C17 | #135 | semidirect |
| 145. C8×D4 | D17 | semidirect |
| 182. C17 | #3284 | semidirect |
| 272. C4 | #10587590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587590 | 2 |
| #11763480 | 2 |
| #11763464 | 2 |
| #11763182 | 2 |
| #11763038 | 2 |
| #11763020 | 2 |
| #11763005 | 2 |
| #11762973 | 2 |
| #11762956 | 2 |
| C4×#63219 | 2 |
| C8×D4×C17 | 2 |
| #3284 | 17 |