Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
182 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 58 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. #26042313 | C2 | semidirect |
| 2. D4×#13089685 | C2 | semidirect |
| 3. #26042142 | C2 | semidirect |
| 4. #26042127 | C2 | semidirect |
| 5. D4⋊#13089685 | C2 | semidirect |
| 6. #13089685⋊C8 | C2 | semidirect |
| 46. #13089685 | D8 | semidirect |
| 60. D4×C181 | M16 | semidirect |
| 83. C181 | #1581 | semidirect |
| 131. D4 | #15668459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042313 | 2 |
| D4×#13089685 | 2 |
| #26042142 | 2 |
| #26042127 | 2 |
| D4⋊#13089685 | 2 |
| #13089685⋊C8 | 2 |
| #26041359 | 2 |
| #1581 | 181 |