Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22601442 | C2 | semidirect |
| 3. #22590069 | C2 | semidirect |
| 4. #22590067 | C2 | semidirect |
| 5. #22588387 | C2 | semidirect |
| 6. #22586438 | C2 | semidirect |
| 7. C71×#1383 | C2 | semidirect |
| 52. C2×C71⋊C16 | D4 | semidirect |
| 65. C2×C16×C71 | D4 | semidirect |
| 187. #1383 | D71 | semidirect |
| 188. C71 | #13076 | semidirect |
| 240. C2×C16 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601442 | 2 |
| #22598003 | 2 |
| #22590069 | 2 |
| #22590067 | 2 |
| #22588387 | 2 |
| #22586438 | 2 |
| C71×#1383 | 2 |
| #13076 | 71 |