Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
316 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 84 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×#19153885 | C2 | semidirect |
| 2. C2×#19153884 | C2 | semidirect |
| 4. #26042153 | C2 | semidirect |
| 13. C2×#15668433 | C4 | semidirect |
| 14. C2×#15668432 | C4 | semidirect |
| 15. C2×#15668432 | C4 | semidirect |
| 20. C2×M16×C181 | C4 | semidirect |
| 78. #13089678 | C22⋊C4 | semidirect |
| 85. C8×C181 | C22⋊C4 | semidirect |
| 113. C181 | #1809 | semidirect |
| 126. C2×M16 | #10624382 | semidirect |
| 199. C8 | C22⋊#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153885 | 2 |
| C2×#19153884 | 2 |
| #26042221 | 2 |
| #26042153 | 2 |
| C2×M16×D181 | 2 |
| #1809 | 181 |