Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
518 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22598289 | C2 | semidirect |
| 4. #22588409 | C2 | semidirect |
| 5. #22586705 | C2 | semidirect |
| 7. C71×#1293 | C2 | semidirect |
| 210. #1293 | D71 | semidirect |
| 211. C71 | #9978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599098 | 2 |
| #22598289 | 2 |
| #22598281 | 2 |
| #22588409 | 2 |
| #22586705 | 2 |
| #22586701 | 2 |
| C71×#1293 | 2 |
| #9978 | 71 |