Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
992 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 309 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 |
| 2. C2×#17984759 | C2 | direct (N × H) |
| 5. C2×#14555769 | C22 | semidirect |
| 7. #17984759 | C22 | direct (N × H) |
| 15. #14555769 | C23 | semidirect |
| 57. C22×C139 | #100 | semidirect |
| 66. C2×C139 | C2×#100 | semidirect |
| 68. C139 | C22×#100 | semidirect |
| 126. C22 | #17984759 | direct (N × H) |
| 135. C2 | C2×#17984759 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555769 | 2 |
| C2×#17984759 | 2 |
| C23×D4×C139 | 2 |
| C22×#100 | 139 |