Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 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. Q8×#11929639 | C2 | semidirect |
| 3. #23778849 | C2 | semidirect |
| 4. #23778843 | C2 | semidirect |
| 6. #23778834 | C2 | semidirect |
| 18. #19099563 | C4 | semidirect |
| 19. #19099562 | C4 | semidirect |
| 20. #19099561 | C4 | semidirect |
| 22. SD16×C317 | C4 | semidirect |
| 31. Dic634 | C2×C4 | semidirect |
| 36. #14579261 | C2×C4 | semidirect |
| 37. Q8×C317 | C2×C4 | semidirect |
| 39. C8×C317 | C2×C4 | semidirect |
| 58. C317 | #440 | semidirect |
| 73. SD16 | #11929639 | semidirect |
| 85. Q8 | C2×#11929639 | semidirect |
| 98. C8 | C2×#11929639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11929639 | 2 |
| D4×#11929639 | 2 |
| #23778849 | 2 |
| #23778843 | 2 |
| #23778842 | 2 |
| #23778834 | 2 |
| SD16×D317 | 2 |
| #440 | 317 |