Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#17984861 | C2 | semidirect |
| 2. #22581382 | C2 | direct (N × H) |
| 3. C2×Dic1112 | C2 | semidirect |
| 4. C2×#17984786 | C2 | semidirect |
| 5. C2×C16×D139 | C2 | semidirect |
| 6. C2×D16×C139 | C2 | semidirect |
| 9. #17984861 | C22 | semidirect |
| 13. Dic1112 | C22 | semidirect |
| 14. #17984786 | C22 | semidirect |
| 16. C16×D139 | C22 | semidirect |
| 18. D16×C139 | C22 | semidirect |
| 64. C2×C139 | #508 | semidirect |
| 67. C139 | C2×#508 | semidirect |
| 73. C2×D16 | D139 | semidirect |
| 84. D16 | C2×D139 | semidirect |
| 133. C2 | #22581382 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984861 | 2 |
| #22581382 | 2 |
| C2×Dic1112 | 2 |
| C2×#17984786 | 2 |
| C2×C16×D139 | 2 |
| C2×D16×C139 | 2 |
| C2×#508 | 139 |