Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
106 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 40 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. #22579968 | C2 | semidirect |
| 2. #22579967 | C2 | semidirect |
| 3. #22579950 | C2 | semidirect |
| 4. #22579945 | C2 | semidirect |
| 5. #22579944 | C2 | semidirect |
| 6. C8×#11764308 | C2 | semidirect |
| 18. #17984553 | C4 | semidirect |
| 19. #17984552 | C4 | semidirect |
| 20. #17984548 | C4 | semidirect |
| 22. SD16×C277 | C4 | semidirect |
| 51. C277 | #443 | semidirect |
| 64. SD16 | #11764308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22579968 | 2 |
| #22579967 | 2 |
| #22579950 | 2 |
| #22579945 | 2 |
| #22579944 | 2 |
| C8×#11764308 | 2 |
| #22579901 | 2 |
| #443 | 277 |