Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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. #26041760 | C2 | semidirect |
| 3. #26041618 | C2 | semidirect |
| 4. #26041613 | C2 | semidirect |
| 5. #26041602 | C2 | semidirect |
| 6. #26041591 | C2 | semidirect |
| 7. #26041321 | C2 | semidirect |
| 8. C2×#19153749 | C2 | semidirect |
| 9. #26041275 | C2 | semidirect |
| 10. #26041247 | C2 | semidirect |
| 11. #417×C181 | C2 | semidirect |
| 133. C181 | #3098 | semidirect |
| 143. #417 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041857 | 2 |
| #26041760 | 2 |
| #26041618 | 2 |
| #26041613 | 2 |
| #26041602 | 2 |
| #26041591 | 2 |
| #26041321 | 2 |
| C2×#19153749 | 2 |
| #26041275 | 2 |
| #26041247 | 2 |
| #417×C181 | 2 |
| #3098 | 181 |