Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
338 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 22. C2×Dic724 | C4 | semidirect |
| 23. C2×#15668439 | C4 | semidirect |
| 24. C2×#15668439 | C4 | semidirect |
| 28. C2×Q16×C181 | C4 | semidirect |
| 80. C2×#10624382 | Q16 | semidirect |
| 137. C181 | #1878 | semidirect |
| 153. C2×Q16 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10624382 | 2 |
| C2×#19153879 | 2 |
| (C2×#10624382)⋊Q8 | 2 |
| #26042153 | 2 |
| (C2×#10624382)⋊C8 | 2 |
| C2×Q16×D181 | 2 |
| #1878 | 181 |