Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
256 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26041333 | C2 | semidirect |
| 3. #26041329 | C2 | semidirect |
| 4. #26041003 | C2 | semidirect |
| 5. #26041002 | C2 | semidirect |
| 6. #26041002 | C2 | semidirect |
| 7. #323×C181 | C2 | semidirect |
| 119. C181 | #1469 | semidirect |
| 127. #323 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153802 | 2 |
| #26041333 | 2 |
| #26041329 | 2 |
| #26041003 | 2 |
| #26041002 | 2 |
| #323×C181 | 2 |
| #1469 | 181 |