Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
406 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22590112 | C2 | semidirect |
| 5. #22589089 | C2 | semidirect |
| 6. #22586421 | C2 | semidirect |
| 7. C71×#1384 | C2 | semidirect |
| 21. #17985808 | C4 | semidirect |
| 43. #14556068 | C2×C4 | semidirect |
| 60. #106×C71 | C2×C4 | semidirect |
| 160. #1384 | D71 | semidirect |
| 162. C71 | #12951 | semidirect |
| 210. #106 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597111 | 2 |
| #22590112 | 2 |
| #22590090 | 2 |
| #22590075 | 2 |
| #22589089 | 2 |
| #22586421 | 2 |
| C71×#1384 | 2 |
| #12951 | 71 |