Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
616 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 274 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. C23×#13089685 | C2 | semidirect |
| 2. D4×#13089685 | C2 | direct (N × H) |
| 3. C2×C4⋊#13089685 | C2 | semidirect |
| 4. C2×C22⋊#13089685 | C2 | semidirect |
| 5. C2×C4×#13089685 | C2 | semidirect |
| 11. C22×#13089685 | C22 | semidirect |
| 12. C4⋊#13089685 | C22 | semidirect |
| 13. C22⋊#13089685 | C22 | semidirect |
| 14. C4×#13089685 | C22 | semidirect |
| 25. C2×#13089685 | D4 | direct (N × H) |
| 41. C2×D4×C181 | C8 | semidirect |
| 46. #13089685 | C2×D4 | direct (N × H) |
| 60. C23×C181 | C2×C8 | semidirect |
| 63. D4×C181 | C2×C8 | semidirect |
| 64. C2×C4×C181 | C2×C8 | semidirect |
| 71. C22×C181 | C22×C8 | semidirect |
| 74. C4×C181 | C22×C8 | semidirect |
| 81. C2×C181 | C8×D4 | semidirect |
| 85. C181 | C2×C8×D4 | semidirect |
| 109. C2×D4 | #13089685 | direct (N × H) |
| 132. C23 | C2×#13089685 | semidirect |
| 135. D4 | C2×#13089685 | direct (N × H) |
| 147. C2×C4 | C2×#13089685 | semidirect |
| 157. C22 | C22×#13089685 | semidirect |
| 165. C4 | C22×#13089685 | semidirect |
| 167. C2 | D4×#13089685 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13089685 | 2 |
| D4×#13089685 | 2 |
| C2×C4⋊#13089685 | 2 |
| C2×C22⋊#13089685 | 2 |
| C2×C4×#13089685 | 2 |
| C2×D4×Dic181 | 2 |
| C2×C8×D4 | 181 |