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. Q8×D724 | C2 | semidirect |
| 2. #26041625 | C2 | semidirect |
| 3. #26041559 | C2 | semidirect |
| 4. #26041471 | C2 | semidirect |
| 5. Q8×#13089678 | C2 | semidirect |
| 6. C4×#15668434 | C2 | semidirect |
| 7. #550×C181 | C2 | semidirect |
| 47. D724 | #41 | semidirect |
| 53. Q8×C181 | D8 | semidirect |
| 81. C181 | #3358 | semidirect |
| 83. #550 | D181 | semidirect |
| 129. Q8 | #15668434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D724 | 2 |
| #26041625 | 2 |
| #26041559 | 2 |
| #26041471 | 2 |
| Q8×#13089678 | 2 |
| C4×#15668434 | 2 |
| #550×C181 | 2 |
| #3358 | 181 |