Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
166 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 69 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. #13092167 | C2 | semidirect |
| 4. Q8⋊(C23⋊C8) | C2 | semidirect |
| 6. #13092138 | C2 | semidirect |
| 7. C8×Q8×C23 | C2 | semidirect |
| 43. Q8×C23 | M16 | semidirect |
| 56. C8×C23 | SD16 | semidirect |
| 74. C8×Q8 | D23 | semidirect |
| 100. C23 | #1583 | semidirect |
| 121. Q8 | #67262 | semidirect |
| 138. C8 | #67274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#67274 | 2 |
| #13092496 | 2 |
| #13092167 | 2 |
| Q8⋊(C23⋊C8) | 2 |
| #13092144 | 2 |
| #13092138 | 2 |
| C8×Q8×C23 | 2 |
| #1583 | 23 |