Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22601476 | C2 | semidirect |
| 2. #22601474 | C2 | semidirect |
| 3. #22598783 | C2 | semidirect |
| 4. #22590067 | C2 | semidirect |
| 5. #22589231 | C2 | semidirect |
| 6. #22586419 | C2 | semidirect |
| 7. C71×#2143 | C2 | semidirect |
| 48. C2×Dic284 | D4 | semidirect |
| 55. C2×D568 | D4 | semidirect |
| 75. C2×C71⋊C16 | D4 | semidirect |
| 92. C2×C16×C71 | D4 | semidirect |
| 239. #2143 | D71 | semidirect |
| 242. C71 | #13340 | semidirect |
| 323. C2×C16 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601476 | 2 |
| #22601474 | 2 |
| #22598783 | 2 |
| #22590067 | 2 |
| #22589231 | 2 |
| #22586419 | 2 |
| C71×#2143 | 2 |
| #13340 | 71 |