Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
376 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×#14555769 | C2 | semidirect |
| 3. C2×#17984770 | C2 | semidirect |
| 4. #22580713 | C2 | semidirect |
| 5. C4×C22⋊C4×C139 | C2 | semidirect |
| 12. #17984821 | C4 | semidirect |
| 13. #17984821 | C4 | semidirect |
| 14. #17984816 | C4 | semidirect |
| 15. #17984816 | C4 | semidirect |
| 35. #14555769 | D4 | semidirect |
| 103. C22×C139 | #104 | semidirect |
| 125. C139 | #1871 | semidirect |
| 130. C4×C22⋊C4 | D139 | semidirect |
| 232. C22 | #17984770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555769 | 2 |
| #22581464 | 2 |
| C2×#17984770 | 2 |
| #22580713 | 2 |
| C4×C22⋊C4×C139 | 2 |
| #1871 | 139 |