Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
398 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22597445 | C2 | semidirect |
| 3. #22587004 | C2 | semidirect |
| 6. #22586239 | C2 | semidirect |
| 7. C71×#1302 | C2 | semidirect |
| 155. #1302 | D71 | semidirect |
| 156. C71 | #9008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598686 | 2 |
| #22597445 | 2 |
| #22587004 | 2 |
| #22586810 | 2 |
| #22586808 | 2 |
| #22586239 | 2 |
| C71×#1302 | 2 |
| #9008 | 71 |