Finite Group DatabasebetaFinite Group DatabasebetaOrder 8896.
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D139 |
| commutator, socle | C22×C139 | C24 |
| Fitting | C22⋊Q8×C139 | C2 |
| hypercenter | C22⋊Q8 | D139 |
| hypocenter | C139 | D4×Q8 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic278 | C2 | semidirect |
| 2. C2×Q8×D139 | C2 | semidirect |
| 3. #17984841 | C2 | semidirect |
| 4. #17984840 | C2 | semidirect |
| 5. #17984822 | C2 | semidirect |
| 6. #17984820 | C2 | semidirect |
| 7. #17984819 | C2 | semidirect |
| 8. #17984807 | C2 | semidirect |
| 11. C22⋊Q8×C139 | C2 | semidirect |
| 41. Dic278 | D4 | semidirect |
| 42. C22⋊D139 | Q8 | semidirect |
| 60. C22×C139 | C2×Q8 | semidirect |
| 64. C2×D139 | C2×Q8 | semidirect |
| 73. Dic139 | C2×Q8 | semidirect |
| 79. C139 | D4×Q8 | semidirect |
| 88. C22⋊Q8 | D139 | semidirect |
| 143. C22 | Q8×D139 | semidirect |