Finite Group DatabasebetaFinite Group DatabasebetaOrder 25856.
1026 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 154 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 | #379 |
| commutator | C22×C4 | C22×C4×C101 |
| Frattini, cosocle | C2×C42 | C23×C101 |
| prime radical | C101×#3496 | C2 |
| LCS | G ▷ C22×C4 ▷ 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×#1955 | C2 | semidirect |
| 3. C101×#1551 | C2 | semidirect |
| 4. C101×#1530 | C2 | semidirect |
| 5. C101×#1466 | C2 | semidirect |
| 15. #432×C101 | C22 | semidirect |
| 16. C2×C4⋊C8×C101 | C22 | semidirect |
| 18. C2×#97×C101 | C22 | semidirect |
| 162. #8456 | C101 | direct (N × H) |
| 170. #1955 | C2×C101 | semidirect |
| 171. #1551 | C2×C101 | semidirect |
| 172. #1530 | C2×C101 | semidirect |
| 173. #1466 | C2×C101 | semidirect |
| 174. C101 | #8456 | direct (N × H) |
| 184. #432 | C22×C101 | semidirect |
| 185. C2×C4⋊C8 | C22×C101 | semidirect |
| 187. C2×#97 | C22×C101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C101×#3496 | 2 |
| C101×#1955 | 2 |
| C101×#1551 | 2 |
| C101×#1530 | 2 |
| C101×#1466 | 2 |
| #8456 | 101 |