Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
414 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. #22590114 | C2 | semidirect |
| 3. #22590067 | C2 | semidirect |
| 4. #22590056 | C2 | semidirect |
| 5. #22589945 | C2 | semidirect |
| 6. #22589238 | C2 | semidirect |
| 7. C71×#1978 | C2 | semidirect |
| 11. C2×#14556072 | C4 | semidirect |
| 12. C2×#14556069 | C4 | semidirect |
| 173. #1978 | D71 | semidirect |
| 175. C71 | #13247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986435 | 2 |
| #22590114 | 2 |
| #22590067 | 2 |
| #22590056 | 2 |
| #22589945 | 2 |
| #22589238 | 2 |
| C71×#1978 | 2 |
| #13247 | 71 |