Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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×D368 | C2 | semidirect |
| 2. C2×#10625008 | C2 | semidirect |
| 3. #13092792 | C2 | semidirect |
| 4. C16×Dic23 | C2 | semidirect |
| 5. C2×C23×D16 | C2 | semidirect |
| 27. C16×C23 | D4 | semidirect |
| 28. C23⋊C16 | D4 | semidirect |
| 49. Dic23 | D16 | semidirect |
| 52. C2×D16 | D23 | semidirect |
| 69. C23 | #2246 | semidirect |
| 82. C16 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D368 | 2 |
| C2×#10625008 | 2 |
| #13092792 | 2 |
| C16×Dic23 | 2 |
| C2×C23×D16 | 2 |
| #2246 | 23 |