Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
200 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #22586406 | C2 | semidirect |
| 5. #22586405 | C2 | semidirect |
| 6. #22586405 | C2 | semidirect |
| 7. C71×#1368 | C2 | semidirect |
| 106. #1368 | D71 | semidirect |
| 107. C71 | #12031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590141 | 2 |
| #22587100 | 2 |
| #22587085 | 2 |
| #22586406 | 2 |
| #22586405 | 2 |
| C71×#1368 | 2 |
| #12031 | 71 |