Finite Group DatabasebetaFinite Group DatabasebetaOrder 25856.
274 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C101 | #1616 |
| commutator, Frattini, cosocle | C2×M16 | C23×C101 |
| prime radical | #469×C101 | C22 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C101 ◁ C2×C4×C101 ◁ C2×M16×C101 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C101×#2239 | C2 | semidirect |
| 4. C101×#2103 | C2 | semidirect |
| 5. C101×#1342 | C2 | semidirect |
| 7. C101×#1328 | C2 | semidirect |
| 132. #12306 | C101 | direct (N × H) |
| 138. #2239 | C2×C101 | semidirect |
| 140. #2103 | C2×C101 | semidirect |
| 141. #1342 | C2×C101 | semidirect |
| 143. #1328 | C2×C101 | semidirect |
| 144. C101 | #12306 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C101×#3263 | 2 |
| C101×#2239 | 2 |
| C101×#2238 | 2 |
| C101×#2103 | 2 |
| C101×#1342 | 2 |
| C101×#1341 | 2 |
| C101×#1328 | 2 |
| #12306 | 101 |