Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
914 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 201 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. #22588636 | C2 | semidirect |
| 3. #22588631 | C2 | semidirect |
| 4. #22588631 | C2 | semidirect |
| 5. #22588631 | C2 | semidirect |
| 6. #22588485 | C2 | semidirect |
| 7. C71×#1840 | C2 | semidirect |
| 159. #1840 | D71 | semidirect |
| 160. C71 | #23358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591621 | 2 |
| #22588636 | 2 |
| #22588631 | 2 |
| #22588485 | 2 |
| C71×#1840 | 2 |
| #23358 | 71 |