Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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. #13092852 | C2 | semidirect |
| 2. C2×#10625008 | C2 | semidirect |
| 3. #13092687 | C2 | semidirect |
| 4. #13092230 | C2 | semidirect |
| 5. #13092224 | C2 | semidirect |
| 6. #13092201 | C2 | semidirect |
| 7. C23×#576 | C2 | semidirect |
| 17. C2×D184 | C22 | semidirect |
| 22. #10625001 | C22 | semidirect |
| 23. #10624994 | C22 | semidirect |
| 24. C2×C23⋊C16 | C22 | semidirect |
| 88. #576 | D23 | semidirect |
| 118. C23 | #2192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092852 | 2 |
| C2×#10625008 | 2 |
| #13092687 | 2 |
| #13092230 | 2 |
| #13092224 | 2 |
| #13092201 | 2 |
| C23×#576 | 2 |
| #2192 | 23 |