Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #11763356 | C2 | semidirect |
| 2. #11763213 | C2 | semidirect |
| 3. #11763184 | C2 | semidirect |
| 4. #11763154 | C2 | semidirect |
| 5. #11763046 | C2 | semidirect |
| 6. #11763044 | C2 | semidirect |
| 7. #11763042 | C2 | semidirect |
| 8. C4×D136 | C2 | semidirect |
| 9. C4×#63228 | C2 | semidirect |
| 10. C4×C8×D17 | C2 | semidirect |
| 11. C4×D8×C17 | C2 | semidirect |
| 96. C4×D17 | D8 | semidirect |
| 99. C8×C17 | #41 | semidirect |
| 101. #3622 | #41 | semidirect |
| 131. C4×D8 | D17 | semidirect |
| 166. C17 | #3169 | semidirect |
| 229. C8 | #63252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763356 | 2 |
| #11763213 | 2 |
| #11763184 | 2 |
| #11763154 | 2 |
| #11763046 | 2 |
| #11763044 | 2 |
| #11763042 | 2 |
| C4×D136 | 2 |
| C4×#63228 | 2 |
| C4×C8×D17 | 2 |
| C4×D8×C17 | 2 |
| #3169 | 17 |