Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. C4⋊Q8×D181 | C2 | semidirect |
| 3. #26041684 | C2 | semidirect |
| 4. #26041682 | C2 | semidirect |
| 5. #26041625 | C2 | semidirect |
| 6. #26041591 | C2 | semidirect |
| 7. #26041557 | C2 | semidirect |
| 8. #26041330 | C2 | semidirect |
| 9. #486×C181 | C2 | semidirect |
| 113. C181 | #3226 | semidirect |
| 120. #486 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041827 | 2 |
| C4⋊Q8×D181 | 2 |
| #26041684 | 2 |
| #26041682 | 2 |
| #26041625 | 2 |
| #26041591 | 2 |
| #26041557 | 2 |
| #26041330 | 2 |
| #486×C181 | 2 |
| #3226 | 181 |