Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#14555775 | C2 | semidirect |
| 4. #22581192 | C2 | direct (N × H) |
| 5. C2×#17984775 | C2 | semidirect |
| 6. C2×#17984766 | C2 | semidirect |
| 7. C2×#17984765 | C2 | semidirect |
| 11. C2×#14555775 | C22 | semidirect |
| 21. #17984775 | C22 | semidirect |
| 22. #17984766 | C22 | semidirect |
| 23. #17984765 | C22 | semidirect |
| 75. C23×C139 | Q16 | semidirect |
| 99. C22×C139 | C2×Q16 | semidirect |
| 111. C2×C139 | #467 | semidirect |
| 115. C139 | C2×#467 | semidirect |
| 182. C23 | #14555775 | semidirect |
| 215. C22 | C2×#14555775 | semidirect |
| 227. C2 | #22581192 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555775 | 2 |
| C23×C139⋊C8 | 2 |
| C2×#17984821 | 2 |
| #22581192 | 2 |
| C2×#17984775 | 2 |
| C2×#17984766 | 2 |
| C2×#17984765 | 2 |
| C2×C22⋊Q8×C139 | 2 |
| C2×#467 | 139 |