Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
1620 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 573 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. C22×#14555511 | C2 | semidirect |
| 2. C22×Q8×D137 | C2 | semidirect |
| 3. #22578065 | C2 | direct (N × H) |
| 4. C2×#17984076 | C2 | semidirect |
| 5. C2×#17984068 | C2 | semidirect |
| 6. C2×#17984063 | C2 | semidirect |
| 7. C2×C4×D548 | C2 | semidirect |
| 8. C2×C4×Q8×C137 | C2 | semidirect |
| 10. C2×#14555511 | C22 | semidirect |
| 13. C2×Q8×D137 | C22 | semidirect |
| 18. #17984076 | C22 | semidirect |
| 19. #17984068 | C22 | semidirect |
| 20. #17984063 | C22 | semidirect |
| 21. C4×D548 | C22 | semidirect |
| 27. C4×Q8×C137 | C22 | semidirect |
| 50. C2×Q8×C137 | D4 | semidirect |
| 62. C22×D137 | #41 | semidirect |
| 75. Q8×C137 | C2×D4 | semidirect |
| 93. C2×D137 | C2×#41 | semidirect |
| 99. C2×C137 | #548 | semidirect |
| 105. C137 | C2×#548 | semidirect |
| 113. C2×C4×Q8 | D137 | semidirect |
| 128. C4×Q8 | C2×D137 | semidirect |
| 142. C2×Q8 | D548 | semidirect |
| 173. Q8 | C2×D548 | semidirect |
| 207. C2 | #22578065 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555511 | 2 |
| C22×Q8×D137 | 2 |
| #22578065 | 2 |
| C2×#17984076 | 2 |
| C2×#17984068 | 2 |
| C2×#17984063 | 2 |
| C2×C4×D548 | 2 |
| C2×C4×Q8×C137 | 2 |
| C2×#548 | 137 |