Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
456 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. D181⋊(C22⋊C8) | C2 | semidirect |
| 2. #26042123 | C2 | semidirect |
| 3. #26042122 | C2 | semidirect |
| 7. C22⋊#13089685 | C22 | semidirect |
| 24. C23×D181 | C8 | semidirect |
| 60. C22×D181 | C2×C8 | semidirect |
| 74. C23×C181 | C2×C8 | semidirect |
| 117. D181 | #323 | semidirect |
| 118. C181 | C2×#323 | semidirect |
| 184. C23 | D181⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊(C22⋊C8) | 2 |
| #26042123 | 2 |
| #26042122 | 2 |
| C2×C22⋊C4×D181 | 2 |
| C2×#323 | 181 |