Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
222 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 46 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 | #353 |
| commutator | C42 | C2×C8×C103 |
| Frattini, cosocle | #423 | C22×C103 |
| socle | C2×C103 | #1318 |
| prime radical | #532×C103 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C103 ◁ C2×C4×C103 ◁ C22×C4×C103 ◁ #423×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C103×#1327 | C2 | semidirect |
| 73. #7357 | C103 | direct (N × H) |
| 79. #1327 | C2×C103 | semidirect |
| 80. C103 | #7357 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C103×#1962 | 2 |
| C103×#1327 | 2 |
| #7357 | 103 |