Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #22586955 | C2 | semidirect |
| 5. #22586240 | C2 | semidirect |
| 6. #22586212 | C2 | semidirect |
| 7. C71×#1485 | C2 | semidirect |
| 197. #1485 | D71 | semidirect |
| 200. C71 | #9312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598496 | 2 |
| #22596769 | 2 |
| #22586955 | 2 |
| #22586775 | 2 |
| #22586240 | 2 |
| #22586212 | 2 |
| C71×#1485 | 2 |
| #9312 | 71 |