Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22581010 | C2 | semidirect |
| 3. #22580682 | C2 | semidirect |
| 4. C4×M16×C139 | C2 | semidirect |
| 13. C4⋊(C139⋊C8) | C22 | semidirect |
| 19. C4×C8×C139 | C22 | semidirect |
| 48. D556 | M16 | semidirect |
| 85. C139 | #1490 | semidirect |
| 89. C4×M16 | D139 | semidirect |
| 105. C4×C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D556 | 2 |
| #22581010 | 2 |
| #22580682 | 2 |
| C4×M16×C139 | 2 |
| #1490 | 139 |