Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#19153815 | C2 | semidirect |
| 3. #26041687 | C2 | semidirect |
| 4. #26041637 | C2 | semidirect |
| 5. #26041610 | C2 | semidirect |
| 6. #26041609 | C2 | semidirect |
| 8. #26041573 | C2 | semidirect |
| 9. #26041567 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 128. C181 | #3238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153815 | 2 |
| #26041810 | 2 |
| #26041687 | 2 |
| #26041637 | 2 |
| #26041610 | 2 |
| #26041609 | 2 |
| #26041590 | 2 |
| #26041573 | 2 |
| #26041567 | 2 |
| #26041333 | 2 |
| #480×C181 | 2 |
| #3238 | 181 |