Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26041951 | C2 | semidirect |
| 2. Q8×D724 | C2 | semidirect |
| 3. #26041626 | C2 | semidirect |
| 4. #26041560 | C2 | semidirect |
| 5. #26041475 | C2 | semidirect |
| 6. C4×D1448 | C2 | semidirect |
| 7. C8×Q8×C181 | C2 | semidirect |
| 52. D724 | #41 | semidirect |
| 57. Q8×C181 | D8 | semidirect |
| 81. C181 | #3358 | semidirect |
| 88. C8×Q8 | D181 | semidirect |
| 129. Q8 | D1448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041951 | 2 |
| Q8×D724 | 2 |
| #26041626 | 2 |
| #26041560 | 2 |
| #26041475 | 2 |
| C4×D1448 | 2 |
| C8×Q8×C181 | 2 |
| #3358 | 181 |