Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22590112 | C2 | semidirect |
| 2. #22590105 | C2 | semidirect |
| 6. #22589118 | C2 | semidirect |
| 7. C71×#1386 | C2 | semidirect |
| 146. #1386 | D71 | semidirect |
| 147. C71 | #13469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590112 | 2 |
| #22590105 | 2 |
| C2×#17985808 | 2 |
| #22590069 | 2 |
| #22589236 | 2 |
| #22589118 | 2 |
| C71×#1386 | 2 |
| #13469 | 71 |