Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22601350 | C2 | semidirect |
| 2. #22590602 | C2 | semidirect |
| 4. #22590398 | C2 | semidirect |
| 5. #22590380 | C2 | semidirect |
| 6. C16×Dic142 | C2 | semidirect |
| 7. #22590186 | C2 | semidirect |
| 8. C4×Q32×C71 | C2 | semidirect |
| 125. C4×Q32 | D71 | semidirect |
| 127. C71 | #33963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601350 | 2 |
| #22590602 | 2 |
| #22590590 | 2 |
| #22590398 | 2 |
| #22590380 | 2 |
| C16×Dic142 | 2 |
| #22590186 | 2 |
| C4×Q32×C71 | 2 |
| #33963 | 71 |