Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
464 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22590550 | C2 | semidirect |
| 3. #22590544 | C2 | semidirect |
| 4. #22590501 | C2 | semidirect |
| 5. #22590449 | C2 | semidirect |
| 6. C4×Dic568 | C2 | semidirect |
| 8. #22590127 | C2 | semidirect |
| 9. C71×#2253 | C2 | semidirect |
| 134. #2253 | D71 | semidirect |
| 142. C71 | #33919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22600707 | 2 |
| #22590550 | 2 |
| #22590544 | 2 |
| #22590501 | 2 |
| #22590449 | 2 |
| C4×Dic568 | 2 |
| #22590173 | 2 |
| #22590127 | 2 |
| C71×#2253 | 2 |
| #33919 | 71 |