Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 3. #26041619 | C2 | semidirect |
| 4. #26041618 | C2 | semidirect |
| 5. #26041613 | C2 | semidirect |
| 6. #26041608 | C2 | semidirect |
| 7. #26041319 | C2 | semidirect |
| 8. #26041317 | C2 | semidirect |
| 9. #26041288 | C2 | semidirect |
| 11. C2×#103×C181 | C2 | semidirect |
| 126. C181 | #3097 | semidirect |
| 137. C2×#103 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041853 | 2 |
| #26041760 | 2 |
| #26041619 | 2 |
| #26041618 | 2 |
| #26041613 | 2 |
| #26041608 | 2 |
| #26041319 | 2 |
| #26041317 | 2 |
| #26041288 | 2 |
| #26041245 | 2 |
| C2×#103×C181 | 2 |
| #3097 | 181 |