Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 105 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. C22×#67262 | C2 | semidirect |
| 3. C2×(C2×D23)⋊C8 | C2 | semidirect |
| 4. C2×(C2×D23)⋊C8 | C2 | semidirect |
| 5. C2×(C2×D23)⋊C8 | C2 | semidirect |
| 6. #13092172 | C2 | semidirect |
| 7. C23×#336 | C2 | semidirect |
| 54. C2×C8×C23 | D4 | semidirect |
| 65. C2×C23⋊C8 | D4 | semidirect |
| 81. C22×D23 | M16 | semidirect |
| 87. C2×C4×C23 | M16 | semidirect |
| 149. #336 | D23 | semidirect |
| 178. C23 | #1870 | semidirect |
| 213. C2×C8 | D92 | semidirect |
| 254. C2×C4 | #67262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67262 | 2 |
| C2×C4×D92 | 2 |
| C2×(C2×D23)⋊C8 | 2 |
| #13092172 | 2 |
| C23×#336 | 2 |
| #1870 | 23 |