Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
432 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 118 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. C23×#3624 | C2 | semidirect |
| 2. C2×C22⋊#3624 | C2 | semidirect |
| 3. C2×C22⋊#3624 | C2 | semidirect |
| 4. #11763675 | C2 | semidirect |
| 25. C2×D4×C17 | C8 | semidirect |
| 45. C2×#3624 | D4 | semidirect |
| 59. C23×C17 | C2×C8 | semidirect |
| 65. C2×C4×C17 | C2×C8 | semidirect |
| 94. C22×C17 | C22⋊C8 | semidirect |
| 134. C17 | #1869 | semidirect |
| 139. C2×D4 | #3624 | semidirect |
| 172. C23 | C2×#3624 | semidirect |
| 195. C2×C4 | C2×#3624 | semidirect |
| 207. C22 | C22⋊#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3624 | 2 |
| C2×C22⋊#3624 | 2 |
| #11763675 | 2 |
| C2×D4×Dic17 | 2 |
| #1869 | 17 |