Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
620 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | #384×C71 | C2 |
| hypercenter | #384 | D71 |
| hypocenter | C71 | #2538 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556108 | C2 | semidirect |
| 2. C2×C4×Dic142 | C2 | semidirect |
| 4. #17985921 | C2 | semidirect |
| 6. #17985898 | C2 | semidirect |
| 7. #17985856 | C2 | semidirect |
| 8. #384×C71 | C2 | semidirect |
| 31. C2×Dic142 | D4 | semidirect |
| 34. C2×D284 | Q8 | semidirect |
| 106. C4×C71 | C22⋊Q8 | semidirect |
| 119. C71 | #2538 | semidirect |
| 126. #384 | D71 | semidirect |
| 228. C4 | #14556108 | semidirect |