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×#17986430 | C2 | semidirect |
| 2. #22598769 | C2 | semidirect |
| 3. #22598767 | C2 | semidirect |
| 4. #22590600 | C2 | semidirect |
| 5. #22590596 | C2 | semidirect |
| 6. #22590592 | C2 | semidirect |
| 7. #22590589 | C2 | semidirect |
| 8. C4×C16×D71 | C2 | semidirect |
| 9. C71×#2248 | C2 | semidirect |
| 65. C16×D71 | D4 | semidirect |
| 159. C4×C71 | #508 | semidirect |
| 176. #2248 | D71 | semidirect |
| 180. C71 | #33713 | semidirect |
| 333. C4 | #17986430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986430 | 2 |
| #22598769 | 2 |
| #22598767 | 2 |
| #22590600 | 2 |
| #22590596 | 2 |
| #22590592 | 2 |
| #22590589 | 2 |
| C4×C16×D71 | 2 |
| C71×#2248 | 2 |
| #33713 | 71 |