Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
546 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #22595299 | C2 | semidirect |
| 2. #22589575 | C2 | semidirect |
| 3. #22589575 | C2 | semidirect |
| 5. #22586164 | C2 | semidirect |
| 6. #22586162 | C2 | semidirect |
| 7. C71×#1270 | C2 | semidirect |
| 97. C4⋊Dic71 | D8 | semidirect |
| 237. #1270 | D71 | semidirect |
| 238. C71 | #7740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22595299 | 2 |
| #22589575 | 2 |
| #22589410 | 2 |
| #22586164 | 2 |
| #22586162 | 2 |
| C71×#1270 | 2 |
| #7740 | 71 |