Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26041614 | C2 | semidirect |
| 4. #26041586 | C2 | semidirect |
| 5. #26041501 | C2 | semidirect |
| 6. #26041435 | C2 | semidirect |
| 8. #26041384 | C2 | semidirect |
| 9. #26041377 | C2 | semidirect |
| 10. #26041336 | C2 | semidirect |
| 11. C2×C4×Q8×C181 | C2 | semidirect |
| 131. C181 | #3117 | semidirect |
| 134. C2×C4×Q8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041813 | 2 |
| #26041614 | 2 |
| #26041597 | 2 |
| #26041586 | 2 |
| #26041501 | 2 |
| #26041435 | 2 |
| #26041418 | 2 |
| #26041384 | 2 |
| #26041377 | 2 |
| #26041336 | 2 |
| C2×C4×Q8×C181 | 2 |
| #3117 | 181 |