Finite Group DatabasebetaFinite Group DatabasebetaOrder 25856.
724 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C101 |
| prime radical | C2×#121×C101 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#451×C101 | C2 | semidirect |
| 4. C101×#1784 | C2 | semidirect |
| 5. C101×#1472 | C2 | semidirect |
| 7. C101×#1298 | C2 | semidirect |
| 208. #9989 | C101 | direct (N × H) |
| 217. C2×#451 | C2×C101 | semidirect |
| 219. #1784 | C2×C101 | semidirect |
| 220. #1472 | C2×C101 | semidirect |
| 222. #1298 | C2×C101 | semidirect |
| 223. C101 | #9989 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C101×#3193 | 2 |
| C2×#451×C101 | 2 |
| C2×#448×C101 | 2 |
| C101×#1784 | 2 |
| C101×#1472 | 2 |
| C101×#1471 | 2 |
| C101×#1298 | 2 |
| #9989 | 101 |