Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
552 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 194 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. C22×#15668458 | C2 | semidirect |
| 2. #26042314 | C2 | direct (N × H) |
| 3. C2×C4⋊#13089685 | C2 | semidirect |
| 4. C2×C22⋊#13089685 | C2 | semidirect |
| 5. C2×C4×#13089685 | C2 | semidirect |
| 8. C2×#15668458 | C22 | semidirect |
| 12. C4⋊#13089685 | C22 | semidirect |
| 13. C22⋊#13089685 | C22 | semidirect |
| 14. C4×#13089685 | C22 | semidirect |
| 25. C2×#13089685 | D4 | semidirect |
| 46. #13089685 | C2×D4 | semidirect |
| 64. C2×C4×C181 | M16 | semidirect |
| 74. C4×C181 | C2×M16 | semidirect |
| 81. C2×C181 | #436 | semidirect |
| 85. C181 | C2×#436 | semidirect |
| 147. C2×C4 | #15668458 | semidirect |
| 165. C4 | C2×#15668458 | semidirect |
| 167. C2 | #26042314 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668458 | 2 |
| #26042314 | 2 |
| C2×C4⋊#13089685 | 2 |
| C2×C22⋊#13089685 | 2 |
| C2×C4×#13089685 | 2 |
| C2×D4×Dic181 | 2 |
| C2×#436 | 181 |