Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
1886 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1886 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C103 | #99 |
| commutator | C23 | C22×C8×C103 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C103 |
| prime radical | C26×C103 | C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C103 ◁ C24×C103 ◁ C22×C22⋊C4×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#323×C103 | C2 | semidirect |
| 3. C103×#1316 | C2 | direct (N × H) |
| 13. #323×C103 | C22 | semidirect |
| 21. C25×C103 | C8 | semidirect |
| 72. C24×C103 | C2×C8 | semidirect |
| 192. C2×#1316 | C103 | direct (N × H) |
| 200. C2×C103 | #1316 | direct (N × H) |
| 204. C2×#323 | C2×C103 | semidirect |
| 205. #1316 | C2×C103 | direct (N × H) |
| 206. C103 | C2×#1316 | direct (N × H) |
| 216. #323 | C22×C103 | semidirect |
| 224. C25 | C8×C103 | semidirect |
| 275. C24 | C2×C8×C103 | semidirect |
| 402. C2 | C103×#1316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#379×C103 | 2 |
| C2×#323×C103 | 2 |
| C103×#1316 | 2 |
| C2×#1316 | 103 |