Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22581682 | C2 | semidirect |
| 3. #22581304 | C2 | semidirect |
| 4. #22581239 | C2 | semidirect |
| 7. C8×Q8×C139 | C2 | semidirect |
| 53. Q8×C139 | SD16 | semidirect |
| 74. C139 | #3359 | semidirect |
| 81. C8×Q8 | D139 | semidirect |
| 122. Q8 | #14555774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581682 | 2 |
| Q8×D556 | 2 |
| #22581304 | 2 |
| #22581239 | 2 |
| #22581159 | 2 |
| C4×#14555774 | 2 |
| C8×Q8×C139 | 2 |
| #3359 | 139 |