Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
302 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26041319 | C2 | semidirect |
| 4. #26041148 | C2 | semidirect |
| 5. #26041047 | C2 | semidirect |
| 6. #26041040 | C2 | semidirect |
| 20. #19153743 | C4 | semidirect |
| 30. #15668433 | C2×C4 | semidirect |
| 43. C4×Dic181 | C2×C4 | semidirect |
| 71. Q8×C181 | C4⋊C4 | semidirect |
| 75. D4×C181 | C4⋊C4 | semidirect |
| 112. C181 | #1859 | semidirect |
| 175. Q8 | #15668428 | semidirect |
| 179. D4 | #15668428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041762 | 2 |
| #26041319 | 2 |
| C2×#19153743 | 2 |
| #26041148 | 2 |
| #26041047 | 2 |
| #26041040 | 2 |
| #417×C181 | 2 |
| #1859 | 181 |