Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
302 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 68 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. #26042290 | C2 | semidirect |
| 4. #26042225 | C2 | semidirect |
| 5. #26042158 | C2 | semidirect |
| 6. #26042150 | C2 | semidirect |
| 25. #19153744 | C4 | semidirect |
| 26. #19153743 | C4 | semidirect |
| 27. #19153742 | C4 | semidirect |
| 28. #104×C181 | C4 | semidirect |
| 58. #15668433 | C2×C4 | semidirect |
| 62. C4×Dic181 | C2×C4 | semidirect |
| 64. M16×C181 | C2×C4 | semidirect |
| 65. C42×C181 | C2×C4 | semidirect |
| 77. Dic362 | C4⋊C4 | semidirect |
| 79. D724 | C4⋊C4 | semidirect |
| 96. Q8×C181 | C4⋊C4 | semidirect |
| 98. D4×C181 | C4⋊C4 | semidirect |
| 131. C181 | #1859 | semidirect |
| 158. #104 | #10624382 | semidirect |
| 180. M16 | C2×#10624382 | semidirect |
| 197. C42 | C2×#10624382 | semidirect |
| 202. Q8 | C4⋊#10624382 | semidirect |
| 209. D4 | C4⋊#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042348 | 2 |
| #26042290 | 2 |
| #26042270 | 2 |
| #26042225 | 2 |
| #26042158 | 2 |
| #26042150 | 2 |
| #104×D181 | 2 |
| #1859 | 181 |