Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
162 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 3. #22579943 | C2 | direct (N × H) |
| 12. C2×Dic554 | C4 | semidirect |
| 15. Q8×D277 | C4 | semidirect |
| 19. C2×Q8×C277 | C4 | semidirect |
| 27. Dic554 | C2×C4 | semidirect |
| 37. Q8×C277 | C2×C4 | semidirect |
| 52. C2×C277 | #103 | semidirect |
| 54. D277 | #103 | semidirect |
| 57. C277 | C2×#103 | semidirect |
| 69. C2×Q8 | #11764308 | semidirect |
| 84. Q8 | C2×#11764308 | semidirect |
| 113. C2 | #22579943 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D277⋊C8 | 2 |
| C2×C4⋊#11764308 | 2 |
| #22579943 | 2 |
| C2×Q8×D277 | 2 |
| C2×#103 | 277 |