Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 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. #22580989 | C2 | semidirect |
| 3. #22580969 | C2 | semidirect |
| 4. #22580927 | C2 | semidirect |
| 5. #22580926 | C2 | semidirect |
| 6. #22580911 | C2 | semidirect |
| 7. #421×C139 | C2 | semidirect |
| 13. C2×#14555775 | C4 | semidirect |
| 14. C2×#14555773 | C4 | semidirect |
| 15. C2×#14555772 | C4 | semidirect |
| 16. C2×#14555770 | C4 | semidirect |
| 132. C139 | #1976 | semidirect |
| 137. #421 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984862 | 2 |
| #22580989 | 2 |
| #22580969 | 2 |
| #22580927 | 2 |
| #22580926 | 2 |
| #22580911 | 2 |
| #421×C139 | 2 |
| #1976 | 139 |