Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
278 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22601493 | C2 | semidirect |
| 2. #22590655 | C2 | semidirect |
| 3. C2×#17985838 | C2 | semidirect |
| 4. #22590460 | C2 | semidirect |
| 5. #22586534 | C2 | semidirect |
| 6. #22586525 | C2 | semidirect |
| 7. C71×#1401 | C2 | semidirect |
| 125. #1401 | D71 | semidirect |
| 126. C71 | #13670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601493 | 2 |
| #22590655 | 2 |
| C2×#17985838 | 2 |
| #22590460 | 2 |
| #22586534 | 2 |
| #22586525 | 2 |
| C71×#1401 | 2 |
| #13670 | 71 |