Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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×#17986432 | C2 | semidirect |
| 2. #22598769 | C2 | semidirect |
| 3. #22590602 | C2 | semidirect |
| 4. #22590597 | C2 | semidirect |
| 5. #22590590 | C2 | semidirect |
| 6. C4×C16×D71 | C2 | semidirect |
| 7. C71×#2247 | C2 | semidirect |
| 42. C16×D71 | D4 | semidirect |
| 107. C4×C71 | #508 | semidirect |
| 121. #2247 | D71 | semidirect |
| 124. C71 | #33713 | semidirect |
| 226. C4 | #17986432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986432 | 2 |
| #22598769 | 2 |
| #22590602 | 2 |
| #22590597 | 2 |
| #22590590 | 2 |
| C4×C16×D71 | 2 |
| C71×#2247 | 2 |
| #33713 | 71 |