Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
166 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22580705 | C2 | semidirect |
| 5. #22580704 | C2 | semidirect |
| 6. #22580703 | C2 | semidirect |
| 7. #335×C139 | C2 | semidirect |
| 53. C139⋊C8 | M16 | semidirect |
| 60. C8×C139 | M16 | semidirect |
| 77. C139 | #1569 | semidirect |
| 83. #335 | D139 | semidirect |
| 138. C8 | #14555768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581009 | 2 |
| #22580975 | 2 |
| C4×#14555768 | 2 |
| #22580705 | 2 |
| #22580704 | 2 |
| #22580703 | 2 |
| #335×C139 | 2 |
| #1569 | 139 |