Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×#19153884 | C2 | semidirect |
| 4. #26042153 | C2 | semidirect |
| 17. C22⋊#13089678 | C4 | semidirect |
| 18. #19153728 | C4 | semidirect |
| 19. C22⋊C8×C181 | C4 | semidirect |
| 40. C2×#13089678 | C2×C4 | semidirect |
| 44. C2×C8×C181 | C2×C4 | semidirect |
| 80. C22×C181 | #106 | semidirect |
| 88. C2×D181 | #106 | semidirect |
| 111. C181 | #1853 | semidirect |
| 130. C22⋊C8 | #10624382 | semidirect |
| 150. C2×C8 | C2×#10624382 | semidirect |
| 205. C22 | #19153884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#10624382 | 2 |
| C2×#19153884 | 2 |
| #26042221 | 2 |
| #26042153 | 2 |
| C22⋊C8×D181 | 2 |
| #1853 | 181 |