Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
394 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 394 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. #22590112 | C2 | semidirect |
| 4. #22589944 | C2 | semidirect |
| 5. #22589256 | C2 | semidirect |
| 7. C71×#2141 | C2 | semidirect |
| 11. C2×#14556074 | C4 | semidirect |
| 12. C2×#14556071 | C4 | semidirect |
| 166. #2141 | D71 | semidirect |
| 170. C71 | #13248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986440 | 2 |
| #22590112 | 2 |
| #22590069 | 2 |
| #22589944 | 2 |
| #22589256 | 2 |
| #22589236 | 2 |
| C71×#2141 | 2 |
| #13248 | 71 |