Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22599465 | C2 | semidirect |
| 2. #22599296 | C2 | semidirect |
| 3. #22598721 | C2 | semidirect |
| 4. #22588001 | C2 | semidirect |
| 5. #22587978 | C2 | semidirect |
| 6. #22587972 | C2 | semidirect |
| 7. #22587940 | C2 | semidirect |
| 8. #22586637 | C2 | semidirect |
| 168. C71 | #19724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599465 | 2 |
| #22599296 | 2 |
| #22598721 | 2 |
| #22588001 | 2 |
| #22587978 | 2 |
| #22587972 | 2 |
| #22587940 | 2 |
| #22586637 | 2 |
| C71×#3184 | 2 |
| #19724 | 71 |