Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 63 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. Q8×C139⋊C8 | C2 | semidirect |
| 4. #22580705 | C2 | semidirect |
| 6. #22580674 | C2 | semidirect |
| 7. Q8⋊C8×C139 | C2 | semidirect |
| 53. Q8×C139 | M16 | semidirect |
| 77. C139 | #1588 | semidirect |
| 83. Q8⋊C8 | D139 | semidirect |
| 121. Q8 | #14555768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C139⋊C8 | 2 |
| C4×#14555772 | 2 |
| #22581030 | 2 |
| #22580705 | 2 |
| #22580682 | 2 |
| #22580674 | 2 |
| Q8⋊C8×C139 | 2 |
| #1588 | 139 |