Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
386 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 386 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. C4×#14556063 | C2 | semidirect |
| 3. #22587095 | C2 | semidirect |
| 6. #22586231 | C2 | semidirect |
| 7. C71×#1299 | C2 | semidirect |
| 181. #1299 | D71 | semidirect |
| 182. C71 | #8672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597301 | 2 |
| C4×#14556063 | 2 |
| #22587095 | 2 |
| #22586780 | 2 |
| #22586777 | 2 |
| #22586231 | 2 |
| C71×#1299 | 2 |
| #8672 | 71 |