Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 354 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. #22590597 | C2 | semidirect |
| 2. #22590596 | C2 | semidirect |
| 3. #22590595 | C2 | semidirect |
| 4. #22587956 | C2 | semidirect |
| 6. C16×C71⋊C8 | C2 | semidirect |
| 7. C71×#2248 | C2 | semidirect |
| 53. C71⋊C16 | D8 | semidirect |
| 65. C16×C71 | D8 | semidirect |
| 84. C71⋊C8 | SD32 | semidirect |
| 103. #2248 | D71 | semidirect |
| 107. C71 | #12517 | semidirect |
| 165. C16 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590597 | 2 |
| #22590596 | 2 |
| #22590595 | 2 |
| #22587956 | 2 |
| #22587954 | 2 |
| C16×C71⋊C8 | 2 |
| C71×#2248 | 2 |
| #12517 | 71 |