Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 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. #22580780 | C2 | semidirect |
| 5. #22580779 | C2 | semidirect |
| 6. #22580778 | C2 | semidirect |
| 7. #367×C139 | C2 | semidirect |
| 11. #17984781 | C4 | semidirect |
| 30. C139⋊C16 | C2×C4 | semidirect |
| 34. C16×C139 | C2×C4 | semidirect |
| 63. C139 | #2159 | semidirect |
| 69. #367 | D139 | semidirect |
| 98. C16 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984781 | 2 |
| #22580990 | 2 |
| #107×D139 | 2 |
| #22580780 | 2 |
| #22580779 | 2 |
| #22580778 | 2 |
| #367×C139 | 2 |
| #2159 | 139 |