Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
618 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#19153744 | C2 | semidirect |
| 3. #26041243 | C2 | semidirect |
| 4. C4×C22⋊C4×C181 | C2 | semidirect |
| 8. C2×#15668449 | C4 | semidirect |
| 10. C22×Dic362 | C4 | semidirect |
| 11. C22×D724 | C4 | semidirect |
| 14. C2×#15668433 | C22 | semidirect |
| 20. C2×C42×C181 | C22 | semidirect |
| 61. Dic362 | C22⋊C4 | semidirect |
| 64. D724 | C22⋊C4 | semidirect |
| 99. C22×C181 | #104 | semidirect |
| 119. C181 | #1789 | semidirect |
| 124. C4×C22⋊C4 | D181 | semidirect |
| 137. C2×C42 | C2×D181 | semidirect |
| 223. C22 | #19153744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668449 | 2 |
| C2×#19153744 | 2 |
| #26041243 | 2 |
| C4×C22⋊C4×C181 | 2 |
| #1789 | 181 |