Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
266 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. C17×#131 | C2 | semidirect |
| 3. #10587634 | C2 | semidirect |
| 4. #10587593 | C2 | semidirect |
| 5. M16×D17 | C2 | semidirect |
| 6. #10587587 | C2 | semidirect |
| 7. C2×C8×D17 | C2 | semidirect |
| 15. M16×C17 | C22 | semidirect |
| 16. C2×C8×C17 | C22 | semidirect |
| 17. #63223 | C22 | semidirect |
| 18. C2×#3622 | C22 | semidirect |
| 19. #63218 | C22 | semidirect |
| 22. C8×D17 | C22 | semidirect |
| 23. C8×D17 | C22 | semidirect |
| 52. D17 | #131 | direct (N × H) |
| 57. #131 | D17 | direct (N × H) |
| 60. C17 | C2×#131 | semidirect |
| 70. M16 | C2×D17 | semidirect |
| 76. C2×C8 | C2×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D17 | 2 |
| C17×#131 | 2 |
| #10587634 | 2 |
| #10587593 | 2 |
| M16×D17 | 2 |
| #10587587 | 2 |
| C2×C8×D17 | 2 |
| C2×#131 | 17 |