Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
434 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 4. #22590060 | C2 | semidirect |
| 5. #22589944 | C2 | semidirect |
| 6. #22588465 | C2 | semidirect |
| 7. C2×#362×C71 | C2 | semidirect |
| 13. #17986384 | C4 | semidirect |
| 14. #17986377 | C4 | semidirect |
| 170. C2×#362 | D71 | semidirect |
| 176. C71 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598829 | 2 |
| #22590077 | 2 |
| #22590067 | 2 |
| #22590060 | 2 |
| #22589944 | 2 |
| #22588465 | 2 |
| C2×#362×C71 | 2 |
| #13216 | 71 |