Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
416 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22589113 | C2 | semidirect |
| 5. #22586743 | C2 | semidirect |
| 6. #22586190 | C2 | semidirect |
| 7. C71×#1550 | C2 | semidirect |
| 179. #1550 | D71 | semidirect |
| 184. C71 | #10553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598716 | 2 |
| #22589113 | 2 |
| #22587009 | 2 |
| C2×#17985742 | 2 |
| #22586743 | 2 |
| #22586190 | 2 |
| C71×#1550 | 2 |
| #10553 | 71 |