Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
612 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 141 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×D79 |
| commutator, socle, cosocle | C23×C79 | C24 |
| Fitting, prime radical | C2×#127×C79 | C2 |
| hypercenter | C2×#127 | D79 |
| hypocenter | C79 | #2709 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14579142 | C2 | semidirect |
| 2. #19098477 | C2 | semidirect |
| 3. #19098477 | C2 | semidirect |
| 4. #19098477 | C2 | semidirect |
| 5. #19098447 | C2 | semidirect |
| 6. #19098443 | C2 | semidirect |
| 7. #19098443 | C2 | semidirect |
| 8. #19098443 | C2 | semidirect |
| 149. C79 | #2709 | semidirect |