Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
456 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 197 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. Q8×#11764049 | C2 | semidirect |
| 2. D4×#11764049 | C2 | semidirect |
| 3. #22578516 | C2 | semidirect |
| 4. C2×C4×#11764049 | C2 | semidirect |
| 31. #14555511 | C8 | semidirect |
| 32. #14555510 | C8 | semidirect |
| 33. #14555509 | C8 | semidirect |
| 37. #41×C137 | C8 | semidirect |
| 39. #11764049 | #41 | direct (N × H) |
| 47. Dic274 | C2×C8 | semidirect |
| 48. D548 | C2×C8 | semidirect |
| 49. C22⋊D137 | C2×C8 | semidirect |
| 50. C2×Dic137 | C2×C8 | semidirect |
| 51. C4×D137 | C2×C8 | semidirect |
| 52. C4×D137 | C2×C8 | semidirect |
| 55. Q8×C137 | C2×C8 | semidirect |
| 56. D4×C137 | C2×C8 | semidirect |
| 57. C2×C4×C137 | C2×C8 | semidirect |
| 76. C137 | C8×#41 | semidirect |
| 99. #41 | #11764049 | direct (N × H) |
| 117. Q8 | C2×#11764049 | semidirect |
| 120. D4 | C2×#11764049 | semidirect |
| 132. C2×C4 | C2×#11764049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11764049 | 2 |
| D4×#11764049 | 2 |
| #22578516 | 2 |
| C2×C4×#11764049 | 2 |
| #41×#10587739 | 2 |
| C8×#41 | 137 |