Finite Group DatabasebetaFinite Group DatabasebetaOrder 25856.
944 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C101 |
| prime radical | #532×C101 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C101×#3165 | C2 | semidirect |
| 4. C101×#1660 | C2 | semidirect |
| 5. C101×#1526 | C2 | semidirect |
| 154. #19078 | C101 | direct (N × H) |
| 160. #3165 | C2×C101 | semidirect |
| 162. #1660 | C2×C101 | semidirect |
| 163. #1526 | C2×C101 | semidirect |
| 165. C101 | #19078 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C101×#3550 | 2 |
| C101×#3165 | 2 |
| C101×#3152 | 2 |
| C101×#1660 | 2 |
| C101×#1526 | 2 |
| C101×#1525 | 2 |
| #19078 | 101 |