Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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. #26042284 | C2 | semidirect |
| 3. C4×C4⋊#10624382 | C2 | semidirect |
| 4. #26042149 | C2 | semidirect |
| 14. Q8×Dic181 | C4 | semidirect |
| 16. C4×D724 | C4 | semidirect |
| 18. #19153778 | C4 | semidirect |
| 23. C4×Q8×C181 | C4 | semidirect |
| 67. D724 | C4⋊C4 | semidirect |
| 83. Q8×C181 | C4⋊C4 | semidirect |
| 106. Dic181 | #104 | semidirect |
| 115. C181 | #1806 | semidirect |
| 125. C4×Q8 | #10624382 | semidirect |
| 177. Q8 | C4⋊#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042284 | 2 |
| C2×#19153881 | 2 |
| C4×C4⋊#10624382 | 2 |
| #26042149 | 2 |
| C4×#15668450 | 2 |
| #1806 | 181 |