Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
380 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 4. #26041563 | C2 | semidirect |
| 5. #26041488 | C2 | semidirect |
| 8. #26041385 | C2 | semidirect |
| 9. #26041383 | C2 | semidirect |
| 127. C181 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041831 | 2 |
| C2×#19153781 | 2 |
| #26041609 | 2 |
| #26041563 | 2 |
| #26041488 | 2 |
| #26041437 | 2 |
| #26041434 | 2 |
| #26041385 | 2 |
| #26041383 | 2 |
| #26041333 | 2 |
| #483×C181 | 2 |
| #3113 | 181 |