Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
492 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 166 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×#10587678 | C2 | semidirect |
| 2. #11763844 | C2 | semidirect |
| 3. #11763840 | C2 | semidirect |
| 4. D4×#3624 | C2 | semidirect |
| 5. #11763810 | C2 | semidirect |
| 6. #11763783 | C2 | semidirect |
| 7. C4×#63243 | C2 | semidirect |
| 49. #63243 | D4 | semidirect |
| 93. C4×C17 | #131 | semidirect |
| 134. C17 | #2935 | semidirect |
| 200. C4 | #10587678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587678 | 2 |
| #11763844 | 2 |
| #11763840 | 2 |
| D4×#3624 | 2 |
| #11763810 | 2 |
| #11763783 | 2 |
| C4×#63243 | 2 |
| #11763357 | 2 |
| #2935 | 17 |