Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26042079 | C2 | semidirect |
| 2. #26041791 | C2 | semidirect |
| 3. #26041297 | C2 | semidirect |
| 4. #26041242 | C2 | semidirect |
| 5. H(3,ℤ/4)×C181 | C2 | semidirect |
| 26. C2×Dic362 | D4 | semidirect |
| 28. C2×D724 | D4 | semidirect |
| 46. C2×C8×C181 | D4 | semidirect |
| 49. C42×C181 | D4 | semidirect |
| 98. C181 | #2010 | semidirect |
| 104. H(3,ℤ/4) | D181 | semidirect |
| 142. C2×C8 | D724 | semidirect |
| 148. C42 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042079 | 2 |
| #26041791 | 2 |
| #26041297 | 2 |
| #26041242 | 2 |
| H(3,ℤ/4)×C181 | 2 |
| #2010 | 181 |