Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 358 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. C4×#14556063 | C2 | semidirect |
| 3. #22587101 | C2 | semidirect |
| 6. #22586211 | C2 | semidirect |
| 7. C71×#1291 | C2 | semidirect |
| 173. #1291 | D71 | semidirect |
| 174. C71 | #8693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597309 | 2 |
| C4×#14556063 | 2 |
| #22587101 | 2 |
| #22586948 | 2 |
| #22586945 | 2 |
| #22586211 | 2 |
| C71×#1291 | 2 |
| #8693 | 71 |