Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
302 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22580993 | C2 | semidirect |
| 4. #22580822 | C2 | semidirect |
| 5. #22580721 | C2 | semidirect |
| 6. #22580714 | C2 | semidirect |
| 20. #17984769 | C4 | semidirect |
| 30. #14555769 | C2×C4 | semidirect |
| 43. C4×Dic139 | C2×C4 | semidirect |
| 71. Q8×C139 | C4⋊C4 | semidirect |
| 75. D4×C139 | C4⋊C4 | semidirect |
| 112. C139 | #1859 | semidirect |
| 175. Q8 | Dic139⋊C4 | semidirect |
| 179. D4 | Dic139⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581436 | 2 |
| #22580993 | 2 |
| C2×#17984769 | 2 |
| #22580822 | 2 |
| #22580721 | 2 |
| #22580714 | 2 |
| #417×C139 | 2 |
| #1859 | 139 |