Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
452 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22601489 | C2 | semidirect |
| 2. #22590659 | C2 | semidirect |
| 3. #22590658 | C2 | semidirect |
| 4. #22590650 | C2 | semidirect |
| 5. #22590649 | C2 | semidirect |
| 6. Q64×D71 | C2 | semidirect |
| 7. #22590633 | C2 | semidirect |
| 8. C2×Q64×C71 | C2 | semidirect |
| 110. C2×Q64 | D71 | semidirect |
| 112. C71 | #33984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601489 | 2 |
| #22590659 | 2 |
| #22590658 | 2 |
| #22590650 | 2 |
| #22590649 | 2 |
| Q64×D71 | 2 |
| #22590633 | 2 |
| C2×Q64×C71 | 2 |
| #33984 | 71 |