Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #13092827 | C2 | semidirect |
| 4. #13092826 | C2 | semidirect |
| 5. #13092823 | C2 | semidirect |
| 6. #13092821 | C2 | semidirect |
| 7. #13092814 | C2 | semidirect |
| 11. C23×#501 | C2 | semidirect |
| 79. #67262 | Q8 | semidirect |
| 102. C8×C23 | C2×Q8 | semidirect |
| 103. C23⋊C8 | C2×Q8 | semidirect |
| 126. #501 | D23 | semidirect |
| 167. C23 | #3165 | semidirect |
| 228. C8 | Q8×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092973 | 2 |
| C4⋊Q8×D23 | 2 |
| #13092827 | 2 |
| #13092826 | 2 |
| #13092823 | 2 |
| #13092821 | 2 |
| #13092814 | 2 |
| #13092458 | 2 |
| #13092456 | 2 |
| #13092369 | 2 |
| C23×#501 | 2 |
| #3165 | 23 |