Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. #13092439 | C2 | semidirect |
| 3. C4×#67262 | C2 | semidirect |
| 4. Q8⋊(C23⋊C8) | C2 | semidirect |
| 5. #13092146 | C2 | semidirect |
| 6. #13092144 | C2 | semidirect |
| 7. C23×Q8⋊C8 | C2 | semidirect |
| 61. Q8×C23 | M16 | semidirect |
| 73. D92 | M16 | semidirect |
| 110. Q8⋊C8 | D23 | semidirect |
| 137. C23 | #1489 | semidirect |
| 172. Q8 | #67262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#67292 | 2 |
| #13092439 | 2 |
| C4×#67262 | 2 |
| Q8⋊(C23⋊C8) | 2 |
| #13092146 | 2 |
| #13092144 | 2 |
| C23×Q8⋊C8 | 2 |
| #1489 | 23 |