Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
388 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 156 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. #11763859 | C2 | semidirect |
| 2. #11763844 | C2 | semidirect |
| 3. #11763841 | C2 | semidirect |
| 4. #11763829 | C2 | semidirect |
| 5. #11763827 | C2 | semidirect |
| 6. #11763812 | C2 | semidirect |
| 7. #11763810 | C2 | semidirect |
| 80. C4×D17 | M16 | semidirect |
| 138. C17 | #2989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763859 | 2 |
| #11763844 | 2 |
| #11763841 | 2 |
| #11763829 | 2 |
| #11763827 | 2 |
| #11763812 | 2 |
| #11763810 | 2 |
| C4×#63254 | 2 |
| #2989 | 17 |