Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 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. #22578119 | C2 | direct (N × H) |
| 2. C2×#17984077 | C2 | semidirect |
| 3. C2×#17984063 | C2 | semidirect |
| 4. C2×C4×D548 | C2 | semidirect |
| 5. C2×#17984046 | C2 | semidirect |
| 6. C2×C4⋊Q8×C137 | C2 | semidirect |
| 10. #17984077 | C22 | semidirect |
| 11. #17984063 | C22 | semidirect |
| 12. C4×D548 | C22 | semidirect |
| 13. #17984046 | C22 | semidirect |
| 19. C4⋊Q8×C137 | C22 | semidirect |
| 69. C2×C137 | #555 | semidirect |
| 73. C137 | C2×#555 | semidirect |
| 76. C2×C4⋊Q8 | D137 | semidirect |
| 85. C4⋊Q8 | C2×D137 | semidirect |
| 144. C2 | #22578119 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578119 | 2 |
| C2×#17984077 | 2 |
| C2×#17984063 | 2 |
| C2×C4×D548 | 2 |
| C2×#17984046 | 2 |
| C2×C4⋊Q8×C137 | 2 |
| C2×#555 | 137 |