Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
234 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C103 | #427 |
| commutator | C2×C8 | C22×C4×C103 |
| Frattini, cosocle | C22×C8 | C23×C103 |
| socle | C2×C103 | #1835 |
| prime radical | C23×C103 | #135 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C103 ◁ #117×C103 ◁ #405×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #346×C103 | C4 | semidirect |
| 12. C4×C16×C103 | C4 | semidirect |
| 70. #12893 | C103 | direct (N × H) |
| 79. C103 | #12893 | direct (N × H) |
| 85. #346 | C4×C103 | semidirect |
| 86. C4×C16 | C4×C103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C103×#2108 | 2 |
| C103×#1833 | 2 |
| C103×#1385 | 2 |
| C103×#1384 | 2 |
| C103×#1382 | 2 |
| #12893 | 103 |