Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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×Q16×D139 | C2 | semidirect |
| 2. C2×#17984787 | C2 | semidirect |
| 3. C2×#17984785 | C2 | semidirect |
| 5. #22580756 | C2 | semidirect |
| 6. (C2×D139)⋊C16 | C2 | semidirect |
| 7. #358×C139 | C2 | semidirect |
| 32. Dic556 | D4 | semidirect |
| 43. Q16×C139 | D4 | semidirect |
| 74. C2×D139 | SD32 | semidirect |
| 86. C139 | #2185 | semidirect |
| 93. #358 | D139 | semidirect |
| 123. Q16 | D556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D139 | 2 |
| C2×#17984787 | 2 |
| C2×#17984785 | 2 |
| #22581190 | 2 |
| #22580756 | 2 |
| (C2×D139)⋊C16 | 2 |
| #358×C139 | 2 |
| #2185 | 139 |