Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
522 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22597141 | C2 | semidirect |
| 2. C2×#17985809 | C2 | semidirect |
| 3. #22590056 | C2 | semidirect |
| 4. #22589217 | C2 | semidirect |
| 5. #22586446 | C2 | semidirect |
| 6. #22586423 | C2 | semidirect |
| 24. #509×C71 | C4 | semidirect |
| 63. C2×D8×C71 | C2×C4 | semidirect |
| 69. M32×C71 | C2×C4 | semidirect |
| 106. Q16×C71 | C22⋊C4 | semidirect |
| 114. D8×C71 | C22⋊C4 | semidirect |
| 192. C71 | #13025 | semidirect |
| 197. #509 | Dic71 | semidirect |
| 226. C2×D8 | C2×Dic71 | semidirect |
| 244. M32 | C2×Dic71 | semidirect |
| 276. Q16 | C22⋊Dic71 | semidirect |
| 284. D8 | C22⋊Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597141 | 2 |
| C2×#17985809 | 2 |
| #22590056 | 2 |
| #22589217 | 2 |
| #22586446 | 2 |
| #22586423 | 2 |
| C2×#509×C71 | 2 |
| #13025 | 71 |