Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
164 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 71 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×#10624980 | C2 | semidirect |
| 2. C2×C16×D23 | C2 | semidirect |
| 4. C4⋊(C23⋊C16) | C2 | semidirect |
| 5. (C2×D23)⋊C16 | C2 | semidirect |
| 6. (C2×D23)⋊C16 | C2 | semidirect |
| 7. C23×#346 | C2 | semidirect |
| 37. C16×C23 | D4 | semidirect |
| 64. C2×D23 | M32 | semidirect |
| 77. #346 | D23 | semidirect |
| 96. C23 | #2168 | semidirect |
| 115. C16 | D92 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10624980 | 2 |
| C2×C16×D23 | 2 |
| C8×D92 | 2 |
| C4⋊(C23⋊C16) | 2 |
| (C2×D23)⋊C16 | 2 |
| C23×#346 | 2 |
| #2168 | 23 |