Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1054 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 403 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 |
|---|---|---|
| 10. C4×#11765855 | C4 | semidirect |
| 56. #11765855 | C42 | semidirect |
| 123. C71 | #20507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11765855 | 2 |
| #22590703 | 2 |
| C4×#14556061 | 2 |
| #22588173 | 2 |
| #22588170 | 2 |
| #22588027 | 2 |
| C71×#2276 | 2 |
| #20507 | 71 |