Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22590493 | C2 | semidirect |
| 4. C8×Dic284 | C2 | semidirect |
| 5. #22586397 | C2 | semidirect |
| 7. C71×#1367 | C2 | semidirect |
| 51. Dic284 | SD16 | semidirect |
| 113. #1367 | D71 | semidirect |
| 116. C71 | #12419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590493 | 2 |
| #22590381 | 2 |
| #22587932 | 2 |
| C8×Dic284 | 2 |
| #22586397 | 2 |
| #22586387 | 2 |
| C71×#1367 | 2 |
| #12419 | 71 |