Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
716 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22588657 | C2 | semidirect |
| 3. C2×#17985732 | C2 | semidirect |
| 4. #22586183 | C2 | semidirect |
| 5. C71×#1442 | C2 | semidirect |
| 53. #95×C71 | D4 | semidirect |
| 230. #1442 | D71 | semidirect |
| 232. C71 | #10403 | semidirect |
| 280. #95 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22594442 | 2 |
| #22588657 | 2 |
| C2×#17985732 | 2 |
| #22586183 | 2 |
| C71×#1442 | 2 |
| #10403 | 71 |