Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
336 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 94 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×#19153884 | C2 | semidirect |
| 3. #26042153 | C2 | semidirect |
| 10. C22×#13089678 | C4 | semidirect |
| 12. C2×C8×D181 | C4 | semidirect |
| 13. C2×C8×D181 | C4 | semidirect |
| 16. C22×C8×C181 | C4 | semidirect |
| 58. #13089678 | C22⋊C4 | semidirect |
| 65. C8×C181 | C22⋊C4 | semidirect |
| 68. C22×C181 | #106 | semidirect |
| 73. C2×D181 | #106 | semidirect |
| 89. C181 | #1807 | semidirect |
| 102. C22×C8 | #10624382 | semidirect |
| 155. C8 | C22⋊#10624382 | semidirect |
| 165. C22 | #19153884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153884 | 2 |
| #26042221 | 2 |
| #26042153 | 2 |
| C22×C8×D181 | 2 |
| #1807 | 181 |