Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1200 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 203 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 |
|---|---|---|
| 4. #22587316 | C2 | direct (N × H) |
| 120. C22×C4×C71 | Q16 | semidirect |
| 151. C2×C4×C71 | C2×Q16 | semidirect |
| 198. C2×C71 | #1605 | semidirect |
| 208. C71 | C2×#1605 | semidirect |
| 309. C22×C4 | Dic284 | semidirect |
| 372. C2×C4 | C2×Dic284 | semidirect |
| 399. C2 | #22587316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986630 | 2 |
| C2×#17986157 | 2 |
| C2×#17985919 | 2 |
| #22587316 | 2 |
| C2×#17985737 | 2 |
| C2×#324×C71 | 2 |
| C2×#1605 | 71 |