Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #22581421 | C2 | semidirect |
| 3. #22580969 | C2 | semidirect |
| 4. C2×#17984768 | C2 | semidirect |
| 5. #22580926 | C2 | semidirect |
| 6. #22580714 | C2 | semidirect |
| 7. #344×C139 | C2 | semidirect |
| 11. #17984875 | C4 | semidirect |
| 13. #17984870 | C4 | semidirect |
| 37. C2×Dic278 | C2×C4 | semidirect |
| 39. C2×D556 | C2×C4 | semidirect |
| 64. M16×C139 | C2×C4 | semidirect |
| 129. C139 | #1906 | semidirect |
| 136. #344 | D139 | semidirect |
| 185. M16 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581753 | 2 |
| #22581421 | 2 |
| #22580969 | 2 |
| C2×#17984768 | 2 |
| #22580926 | 2 |
| #22580714 | 2 |
| #344×C139 | 2 |
| #1906 | 139 |