Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#17984873 | C2 | semidirect |
| 3. #22581345 | C2 | semidirect |
| 4. #22581332 | C2 | semidirect |
| 5. #22581327 | C2 | semidirect |
| 6. C4×#14555769 | C2 | semidirect |
| 7. C2×C4⋊Q8×C139 | C2 | semidirect |
| 34. #14555769 | D4 | semidirect |
| 76. C4×C139 | #137 | semidirect |
| 83. C139 | #3152 | semidirect |
| 87. C2×C4⋊Q8 | D139 | semidirect |
| 161. C4 | #17984873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984873 | 2 |
| #22581503 | 2 |
| #22581345 | 2 |
| #22581332 | 2 |
| #22581327 | 2 |
| C4×#14555769 | 2 |
| C2×C4⋊Q8×C139 | 2 |
| #3152 | 139 |