Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
244 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22590171 | C2 | semidirect |
| 2. D4×C71⋊C16 | C2 | semidirect |
| 4. #22586409 | C2 | semidirect |
| 5. #22586296 | C2 | semidirect |
| 6. #22586256 | C2 | semidirect |
| 7. C71×D4⋊C16 | C2 | semidirect |
| 58. C71⋊C16 | D8 | semidirect |
| 74. D4×C71 | M32 | semidirect |
| 119. D4⋊C16 | D71 | semidirect |
| 121. C71 | #12038 | semidirect |
| 190. D4 | #14556067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590171 | 2 |
| D4×C71⋊C16 | 2 |
| C8×#11765850 | 2 |
| #22586409 | 2 |
| #22586296 | 2 |
| #22586256 | 2 |
| C71×D4⋊C16 | 2 |
| #12038 | 71 |