Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
688 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 215 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. #22588836 | C2 | semidirect |
| 2. #22588815 | C2 | semidirect |
| 3. #22588734 | C2 | semidirect |
| 5. #22588489 | C2 | semidirect |
| 20. #497×C71 | C4 | semidirect |
| 21. #494×C71 | C4 | semidirect |
| 22. #492×C71 | C4 | semidirect |
| 134. C71 | #23360 | semidirect |
| 140. #497 | Dic71 | semidirect |
| 141. #494 | Dic71 | semidirect |
| 142. #492 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588836 | 2 |
| #22588815 | 2 |
| #22588734 | 2 |
| #22588724 | 2 |
| #22588489 | 2 |
| C71×#3152 | 2 |
| #23360 | 71 |