Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
306 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #22589944 | C2 | semidirect |
| 5. #22589118 | C2 | semidirect |
| 6. #22586456 | C2 | semidirect |
| 7. C71×#1386 | C2 | semidirect |
| 15. #17985816 | C4 | semidirect |
| 16. #17985813 | C4 | semidirect |
| 146. #1386 | D71 | semidirect |
| 147. C71 | #13156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590090 | 2 |
| C2×#17985808 | 2 |
| #22589944 | 2 |
| #22589236 | 2 |
| #22589118 | 2 |
| #22586456 | 2 |
| C71×#1386 | 2 |
| #13156 | 71 |