Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 229 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. #22580994 | C2 | direct (N × H) |
| 5. C2×#17984775 | C2 | semidirect |
| 6. C2×#17984774 | C2 | semidirect |
| 7. C2×#17984773 | C2 | semidirect |
| 8. C2×#107×C139 | C2 | semidirect |
| 11. C2×#14555768 | C4 | semidirect |
| 23. #17984775 | C22 | semidirect |
| 24. #17984774 | C22 | semidirect |
| 25. #17984773 | C22 | semidirect |
| 29. #107×C139 | C22 | semidirect |
| 40. #14555768 | C2×C4 | semidirect |
| 41. C2×C139⋊C8 | C2×C4 | semidirect |
| 53. C2×C8×C139 | C2×C4 | semidirect |
| 73. C139⋊C8 | C22×C4 | semidirect |
| 83. C8×C139 | C22×C4 | semidirect |
| 100. C2×C139 | #428 | semidirect |
| 105. C139 | C2×#428 | semidirect |
| 112. C2×#107 | D139 | semidirect |
| 133. #107 | C2×D139 | semidirect |
| 152. C2×C8 | C4×D139 | semidirect |
| 189. C8 | C2×C4×D139 | semidirect |
| 207. C2 | #22580994 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555768 | 2 |
| C2×#17984800 | 2 |
| C2×C4⋊C4×D139 | 2 |
| #22580994 | 2 |
| C2×#17984775 | 2 |
| C2×#17984774 | 2 |
| C2×#17984773 | 2 |
| C2×#107×C139 | 2 |
| C2×#428 | 139 |