Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
332 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 92 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×C22⋊#3624 | C2 | semidirect |
| 2. #11763654 | C2 | semidirect |
| 3. #11763652 | C2 | semidirect |
| 21. C2×D4×C17 | C8 | semidirect |
| 48. C23×C17 | C2×C8 | semidirect |
| 54. C2×C4×C17 | C2×C8 | semidirect |
| 114. C17 | #1459 | semidirect |
| 119. C2×D4 | #3624 | semidirect |
| 145. C23 | C2×#3624 | semidirect |
| 165. C2×C4 | C2×#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#3624 | 2 |
| #11763654 | 2 |
| #11763652 | 2 |
| C2×D4×Dic17 | 2 |
| #1459 | 17 |