Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
346 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 144 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. #11763860 | C2 | semidirect |
| 2. #11763842 | C2 | semidirect |
| 3. #11763840 | C2 | semidirect |
| 4. #11763838 | C2 | semidirect |
| 5. #11763833 | C2 | semidirect |
| 6. #11763831 | C2 | semidirect |
| 7. #11763815 | C2 | semidirect |
| 8. #11763814 | C2 | semidirect |
| 151. C17 | #2995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763860 | 2 |
| #11763842 | 2 |
| #11763840 | 2 |
| #11763838 | 2 |
| #11763833 | 2 |
| #11763831 | 2 |
| #11763815 | 2 |
| #11763814 | 2 |
| #11763338 | 2 |
| #2995 | 17 |