Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#17984864 | C2 | semidirect |
| 2. #22581383 | C2 | direct (N × H) |
| 3. C2×#17984788 | C2 | semidirect |
| 4. C2×#17984786 | C2 | semidirect |
| 5. C2×#17984785 | C2 | semidirect |
| 6. C2×#17984783 | C2 | semidirect |
| 7. C22×C139⋊C16 | C2 | semidirect |
| 8. C2×#135×C139 | C2 | semidirect |
| 11. #17984864 | C22 | semidirect |
| 15. #17984788 | C22 | semidirect |
| 16. #17984786 | C22 | semidirect |
| 17. #17984785 | C22 | semidirect |
| 18. #17984783 | C22 | semidirect |
| 21. C2×C139⋊C16 | C22 | semidirect |
| 24. #135×C139 | C22 | semidirect |
| 96. C2×C139 | #508 | semidirect |
| 99. C139 | C2×#508 | semidirect |
| 102. C2×#135 | D139 | semidirect |
| 114. #135 | C2×D139 | semidirect |
| 197. C2 | #22581383 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984864 | 2 |
| #22581383 | 2 |
| C2×#17984788 | 2 |
| C2×#17984786 | 2 |
| C2×#17984785 | 2 |
| C2×#17984783 | 2 |
| C22×C139⋊C16 | 2 |
| C2×#135×C139 | 2 |
| C2×#508 | 139 |