Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
284 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 54 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. #26042186 | C2 | semidirect |
| 3. #26042185 | C2 | semidirect |
| 8. C2×Q8×D181 | C4 | semidirect |
| 12. #19153803 | C4 | semidirect |
| 15. C42×D181 | C4 | semidirect |
| 16. #124×C181 | C4 | semidirect |
| 22. C2×Dic362 | C2×C4 | semidirect |
| 36. C4×Dic181 | C2×C4 | semidirect |
| 37. C2×Q8×C181 | C2×C4 | semidirect |
| 40. C42×C181 | C2×C4 | semidirect |
| 88. D181 | #354 | semidirect |
| 89. C181 | C2×#354 | semidirect |
| 101. #124 | #10624382 | semidirect |
| 112. C2×Q8 | C2×#10624382 | semidirect |
| 130. C42 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊#99 | 2 |
| #26042186 | 2 |
| #26042185 | 2 |
| #124×D181 | 2 |
| C2×#354 | 181 |