Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
566 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#17986440 | C2 | semidirect |
| 2. C22×#14556071 | C2 | semidirect |
| 4. C2×#17985811 | C2 | semidirect |
| 5. C2×#17985805 | C2 | semidirect |
| 6. #22586429 | C2 | semidirect |
| 7. C71×#1979 | C2 | semidirect |
| 58. #14556068 | D4 | semidirect |
| 62. C2×C71⋊C16 | D4 | semidirect |
| 69. C2×Q16×C71 | D4 | semidirect |
| 207. #1979 | D71 | semidirect |
| 209. C71 | #13338 | semidirect |
| 248. C2×Q16 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986440 | 2 |
| C22×#14556071 | 2 |
| #22598826 | 2 |
| C2×#17985811 | 2 |
| C2×#17985805 | 2 |
| #22586429 | 2 |
| C71×#1979 | 2 |
| #13338 | 71 |