Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
402 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 148 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. #11763844 | C2 | semidirect |
| 2. #11763840 | C2 | semidirect |
| 3. D4×#3624 | C2 | semidirect |
| 4. #11763831 | C2 | semidirect |
| 5. #11763827 | C2 | semidirect |
| 6. #11763782 | C2 | semidirect |
| 120. C17 | #2981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763844 | 2 |
| #11763840 | 2 |
| D4×#3624 | 2 |
| #11763831 | 2 |
| #11763827 | 2 |
| #11763782 | 2 |
| #11763357 | 2 |
| #2981 | 17 |