Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#19153838 | C2 | semidirect |
| 2. C2×#19153836 | C2 | semidirect |
| 3. #26041825 | C2 | semidirect |
| 4. #26041664 | C2 | semidirect |
| 5. #26041662 | C2 | semidirect |
| 6. #26041660 | C2 | semidirect |
| 7. #26041657 | C2 | semidirect |
| 8. #26041654 | C2 | semidirect |
| 9. #26041650 | C2 | semidirect |
| 10. C2×C8×Dic181 | C2 | semidirect |
| 11. C2×#135×C181 | C2 | semidirect |
| 55. C2×#13089678 | D4 | semidirect |
| 74. C2×C8×C181 | D4 | semidirect |
| 119. Dic181 | #135 | semidirect |
| 125. C181 | #3147 | semidirect |
| 129. C2×#135 | D181 | semidirect |
| 194. C2×C8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153838 | 2 |
| C2×#19153836 | 2 |
| #26041825 | 2 |
| #26041664 | 2 |
| #26041662 | 2 |
| #26041660 | 2 |
| #26041657 | 2 |
| #26041654 | 2 |
| #26041650 | 2 |
| C2×C8×Dic181 | 2 |
| C2×#135×C181 | 2 |
| #3147 | 181 |