Finite Group DatabasebetaFinite Group DatabasebetaOrder 8896.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D139 |
| commutator | C22×C139 | C24 |
| Frattini | C22 | C23×D139 |
| Fitting | C2×C22⋊C4×C139 | C2 |
| socle | C23×C139 | C23 |
| hypercenter | C2×C22⋊C4 | D139 |
| hypocenter | C139 | C2×C22⋊Q8 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic278 | C2 | semidirect |
| 3. #17984819 | C2 | direct (N × H) |
| 4. C2×C4⋊Dic139 | C2 | semidirect |
| 5. C2×Dic139⋊C4 | C2 | semidirect |
| 6. C2×Dic139⋊C4 | C2 | semidirect |
| 10. C2×Dic278 | C22 | semidirect |
| 17. C4⋊Dic139 | C22 | semidirect |
| 18. Dic139⋊C4 | C22 | semidirect |
| 19. Dic139⋊C4 | C22 | semidirect |
| 37. C23×C139 | Q8 | semidirect |
| 49. C22×C139 | C2×Q8 | semidirect |
| 59. C2×C139 | C22⋊Q8 | semidirect |
| 63. C139 | C2×C22⋊Q8 | semidirect |
| 91. C23 | Dic278 | semidirect |
| 113. C22 | C2×Dic278 | semidirect |
| 123. C2 | #17984819 | direct (N × H) |