Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22581436 | C2 | semidirect |
| 3. #22580959 | C2 | semidirect |
| 4. #22580855 | C2 | semidirect |
| 5. #22580721 | C2 | semidirect |
| 6. #22580713 | C2 | semidirect |
| 7. C2×#104×C139 | C2 | semidirect |
| 10. #17984867 | C4 | semidirect |
| 34. C2×D556 | C2×C4 | semidirect |
| 40. #14555769 | C2×C4 | semidirect |
| 85. Q8×C139 | C22⋊C4 | semidirect |
| 89. D4×C139 | C22⋊C4 | semidirect |
| 132. C139 | #1883 | semidirect |
| 136. C2×#104 | D139 | semidirect |
| 208. Q8 | (C2×D139)⋊C4 | semidirect |
| 216. D4 | (C2×D139)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984867 | 2 |
| #22581436 | 2 |
| #22580959 | 2 |
| #22580855 | 2 |
| #22580721 | 2 |
| #22580713 | 2 |
| C2×#104×C139 | 2 |
| #1883 | 139 |