Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
618 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 90 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×#19153881 | C2 | semidirect |
| 2. #26042250 | C2 | semidirect |
| 3. C4×C22⋊#10624382 | C2 | semidirect |
| 5. C2×#15668459 | C22 | semidirect |
| 7. C2×C4×#10624382 | C22 | semidirect |
| 15. C2×#15668450 | C4 | semidirect |
| 18. C22×D724 | C4 | semidirect |
| 21. C22×Q8×C181 | C4 | semidirect |
| 72. D724 | C22⋊C4 | semidirect |
| 85. Q8×C181 | C22⋊C4 | semidirect |
| 93. C22×C181 | #104 | semidirect |
| 119. C181 | #1789 | semidirect |
| 130. C22×Q8 | #10624382 | semidirect |
| 187. Q8 | C22⋊#10624382 | semidirect |
| 224. C22 | #19153881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153881 | 2 |
| #26042250 | 2 |
| C4×C22⋊#10624382 | 2 |
| C22×#15668450 | 2 |
| #1789 | 181 |