Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#17984770 | C2 | semidirect |
| 3. #22580952 | C2 | semidirect |
| 4. C2×#17984759 | C2 | semidirect |
| 5. #390×C139 | C2 | semidirect |
| 8. #17984887 | C4 | semidirect |
| 13. C2×#14555769 | C22 | semidirect |
| 19. C2×C4⋊C4×C139 | C22 | semidirect |
| 21. C2×C42×C139 | C22 | semidirect |
| 58. Dic278 | C22⋊C4 | semidirect |
| 60. D556 | C22⋊C4 | semidirect |
| 112. C139 | #1792 | semidirect |
| 118. #390 | D139 | semidirect |
| 128. C2×C4⋊C4 | C2×D139 | semidirect |
| 130. C2×C42 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984887 | 2 |
| C2×#17984770 | 2 |
| #22580952 | 2 |
| C2×#17984759 | 2 |
| #390×C139 | 2 |
| #1792 | 139 |