Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
216 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22590178 | C2 | semidirect |
| 3. #22586416 | C2 | semidirect |
| 4. #22586314 | C2 | semidirect |
| 5. C8×C16×C71 | C2 | semidirect |
| 18. Dic568 | C8 | semidirect |
| 19. #14556073 | C8 | semidirect |
| 20. D1136 | C8 | semidirect |
| 76. C8×C16 | D71 | semidirect |
| 77. C71 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590222 | 2 |
| #22590178 | 2 |
| #22586416 | 2 |
| #22586314 | 2 |
| C8×C16×C71 | 2 |
| #12046 | 71 |