Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
518 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 102 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×C103 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C103 |
| prime radical | C2×#121×C103 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C103×#3095 | C2 | semidirect |
| 4. C103×#1818 | C2 | semidirect |
| 5. C103×#1472 | C2 | semidirect |
| 7. C103×#1293 | C2 | semidirect |
| 196. #9978 | C103 | direct (N × H) |
| 205. #3095 | C2×C103 | semidirect |
| 207. #1818 | C2×C103 | semidirect |
| 208. #1472 | C2×C103 | semidirect |
| 210. #1293 | C2×C103 | semidirect |
| 211. C103 | #9978 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C103×#3187 | 2 |
| C103×#3095 | 2 |
| C103×#3094 | 2 |
| C103×#1818 | 2 |
| C103×#1472 | 2 |
| C103×#1471 | 2 |
| C103×#1293 | 2 |
| #9978 | 103 |