Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #26041658 | C2 | semidirect |
| 3. #26041629 | C2 | semidirect |
| 4. #26041486 | C2 | semidirect |
| 68. C2×C4×C181 | Q16 | semidirect |
| 92. C181 | #3209 | semidirect |
| 160. C2×C4 | #15668439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041836 | 2 |
| #26041658 | 2 |
| #26041629 | 2 |
| #26041486 | 2 |
| #26041435 | 2 |
| #26041332 | 2 |
| C2×C4⋊Q8×C181 | 2 |
| #3209 | 181 |