Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
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. #26041301 | C2 | semidirect |
| 3. C4×#15668432 | C2 | semidirect |
| 4. Q8⋊#13089678 | C2 | semidirect |
| 5. #26041008 | C2 | semidirect |
| 6. #26041006 | C2 | semidirect |
| 7. Q8⋊C8×C181 | C2 | semidirect |
| 62. D724 | M16 | semidirect |
| 79. Q8×C181 | M16 | semidirect |
| 110. C181 | #1489 | semidirect |
| 116. Q8⋊C8 | D181 | semidirect |
| 172. Q8 | #15668432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668450 | 2 |
| #26041301 | 2 |
| C4×#15668432 | 2 |
| Q8⋊#13089678 | 2 |
| #26041008 | 2 |
| #26041006 | 2 |
| Q8⋊C8×C181 | 2 |
| #1489 | 181 |