Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #22596738 | C2 | semidirect |
| 5. #22587024 | C2 | semidirect |
| 6. #22587020 | C2 | semidirect |
| 7. C71×#1276 | C2 | semidirect |
| 112. C42×C71 | SD16 | semidirect |
| 181. #1276 | D71 | semidirect |
| 182. C71 | #10283 | semidirect |
| 287. C42 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599470 | 2 |
| #22599267 | 2 |
| #22596738 | 2 |
| #22589168 | 2 |
| #22587024 | 2 |
| #22587020 | 2 |
| C71×#1276 | 2 |
| #10283 | 71 |