Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. #22580758 | C2 | semidirect |
| 5. #22580757 | C2 | semidirect |
| 6. #22580756 | C2 | semidirect |
| 7. #358×C139 | C2 | semidirect |
| 12. Q16×D139 | C4 | semidirect |
| 77. C139 | #2141 | semidirect |
| 85. #358 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D139 | 2 |
| C2×#17984781 | 2 |
| #22580990 | 2 |
| #22580758 | 2 |
| #22580757 | 2 |
| #22580756 | 2 |
| #358×C139 | 2 |
| #2141 | 139 |