Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
442 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22596332 | C2 | semidirect |
| 4. #22586371 | C2 | semidirect |
| 5. #22586370 | C2 | semidirect |
| 6. #22586273 | C2 | semidirect |
| 73. C2×Dic142 | SD16 | semidirect |
| 197. C71 | #12130 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596332 | 2 |
| #22589387 | 2 |
| #22587309 | 2 |
| #22586371 | 2 |
| #22586370 | 2 |
| #22586273 | 2 |
| C71×#1604 | 2 |
| #12130 | 71 |