Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
472 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 162 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. C2×#17984176 | C2 | semidirect |
| 2. C2×#17984175 | C2 | semidirect |
| 3. #22578446 | C2 | direct (N × H) |
| 4. C2×#17984158 | C2 | semidirect |
| 5. C2×#17984153 | C2 | semidirect |
| 6. C2×#17984152 | C2 | semidirect |
| 7. C2×C8×#10587739 | C2 | semidirect |
| 10. #17984176 | C22 | semidirect |
| 12. #17984175 | C22 | semidirect |
| 21. #17984158 | C22 | semidirect |
| 22. #17984153 | C22 | semidirect |
| 23. #17984152 | C22 | semidirect |
| 24. C8×#10587739 | C22 | semidirect |
| 27. #17984109 | C4 | semidirect |
| 29. C2×#14555500 | C4 | semidirect |
| 30. C2×#14555499 | C4 | semidirect |
| 31. C2×#14555495 | C4 | semidirect |
| 33. C2×SD16×C137 | C4 | semidirect |
| 66. #14555500 | C2×C4 | semidirect |
| 67. #14555499 | C2×C4 | semidirect |
| 68. #14555495 | C2×C4 | semidirect |
| 74. SD16×C137 | C2×C4 | semidirect |
| 127. C2×C137 | #443 | semidirect |
| 132. C137 | C2×#443 | semidirect |
| 148. C2×SD16 | #10587739 | semidirect |
| 187. SD16 | C2×#10587739 | semidirect |
| 263. C2 | #22578446 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984176 | 2 |
| C2×#17984175 | 2 |
| #22578446 | 2 |
| C2×#17984158 | 2 |
| C2×#17984153 | 2 |
| C2×#17984152 | 2 |
| C2×C8×#10587739 | 2 |
| C2×#17984109 | 2 |
| C2×#443 | 137 |