Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#14555774 | C2 | semidirect |
| 3. C2×#17984764 | C2 | semidirect |
| 4. #22580859 | C2 | semidirect |
| 5. #336×C139 | C2 | semidirect |
| 22. C2×Dic278 | D4 | semidirect |
| 40. C2×C8×C139 | D4 | semidirect |
| 62. C2×C4×C139 | SD16 | semidirect |
| 89. C139 | #2014 | semidirect |
| 95. #336 | D139 | semidirect |
| 129. C2×C8 | D556 | semidirect |
| 152. C2×C4 | #14555774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555774 | 2 |
| C2×#17984839 | 2 |
| C2×#17984764 | 2 |
| #22580859 | 2 |
| #336×C139 | 2 |
| #2014 | 139 |