Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
192 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 57 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. D4×#11764049 | C2 | semidirect |
| 2. #22578492 | C2 | semidirect |
| 3. D4⋊#11764049 | C2 | semidirect |
| 4. #22578487 | C2 | semidirect |
| 26. D1096 | C8 | semidirect |
| 27. #14555495 | C8 | semidirect |
| 29. D8×C137 | C8 | semidirect |
| 40. D548 | C2×C8 | semidirect |
| 43. #11764040 | C2×C8 | semidirect |
| 44. D4×C137 | C2×C8 | semidirect |
| 45. C8×C137 | C2×C8 | semidirect |
| 61. C137 | #1580 | semidirect |
| 82. D8 | #11764049 | semidirect |
| 95. D4 | C2×#11764049 | semidirect |
| 107. C8 | C2×#11764049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11764049 | 2 |
| #22578492 | 2 |
| D4⋊#11764049 | 2 |
| #22578487 | 2 |
| D8×#10587739 | 2 |
| #1580 | 137 |