Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26042015 | C2 | semidirect |
| 2. D4×Dic362 | C2 | semidirect |
| 3. #26041637 | C2 | semidirect |
| 4. #26041625 | C2 | semidirect |
| 5. #26041567 | C2 | semidirect |
| 6. #26041565 | C2 | semidirect |
| 7. #26041492 | C2 | semidirect |
| 8. #26041406 | C2 | semidirect |
| 9. #26041391 | C2 | semidirect |
| 10. C4×#15668437 | C2 | semidirect |
| 124. C181 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042015 | 2 |
| D4×Dic362 | 2 |
| #26041637 | 2 |
| #26041625 | 2 |
| #26041567 | 2 |
| #26041565 | 2 |
| #26041492 | 2 |
| #26041406 | 2 |
| #26041391 | 2 |
| C4×#15668437 | 2 |
| #459×C181 | 2 |
| #3373 | 181 |