Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22580996 | C2 | semidirect |
| 5. #22580823 | C2 | semidirect |
| 6. #22580721 | C2 | semidirect |
| 7. #339×C139 | C2 | semidirect |
| 20. #17984770 | C4 | semidirect |
| 38. #14555769 | C2×C4 | semidirect |
| 58. C42×C139 | C2×C4 | semidirect |
| 61. Dic278 | C4⋊C4 | semidirect |
| 63. D556 | C4⋊C4 | semidirect |
| 112. C139 | #1859 | semidirect |
| 120. #339 | D139 | semidirect |
| 171. C42 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581433 | 2 |
| #22580996 | 2 |
| C2×#17984770 | 2 |
| #22580955 | 2 |
| #22580823 | 2 |
| #22580721 | 2 |
| #339×C139 | 2 |
| #1859 | 139 |