Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1144 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 258 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. #26042222 | C2 | direct (N × H) |
| 3. C2×(C2×#10624382)⋊C4 | C2 | semidirect |
| 8. (C2×#10624382)⋊C4 | C22 | semidirect |
| 10. C23×Dic181 | C4 | semidirect |
| 12. C22×C4×D181 | C4 | semidirect |
| 13. C22×C4×D181 | C4 | semidirect |
| 16. C23×C4×C181 | C4 | semidirect |
| 29. C22×Dic181 | C2×C4 | semidirect |
| 35. C2×C4×D181 | C2×C4 | semidirect |
| 40. C22×C4×C181 | C2×C4 | semidirect |
| 89. C2×C181 | #381 | semidirect |
| 93. D181 | #381 | semidirect |
| 95. C181 | C2×#381 | semidirect |
| 109. C23×C4 | #10624382 | semidirect |
| 135. C22×C4 | C2×#10624382 | semidirect |
| 188. C2 | #26042222 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#10624382 | 2 |
| #26042222 | 2 |
| C2×(C2×#10624382)⋊C4 | 2 |
| C23×C4×D181 | 2 |
| C2×#381 | 181 |