Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 57 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×#17984785 | C2 | semidirect |
| 2. C2×#17984783 | C2 | semidirect |
| 3. #22581189 | C2 | semidirect |
| 4. #22580757 | C2 | semidirect |
| 5. #22580754 | C2 | semidirect |
| 6. C22⋊(C139⋊C16) | C2 | semidirect |
| 7. C2×#135×C139 | C2 | semidirect |
| 39. Q16×C139 | D4 | semidirect |
| 42. D8×C139 | D4 | semidirect |
| 89. C139 | #2186 | semidirect |
| 91. C2×#135 | D139 | semidirect |
| 123. Q16 | C22⋊D139 | semidirect |
| 128. D8 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984785 | 2 |
| C2×#17984783 | 2 |
| #22581189 | 2 |
| #22580757 | 2 |
| #22580754 | 2 |
| C22⋊(C139⋊C16) | 2 |
| C2×#135×C139 | 2 |
| #2186 | 139 |