Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
344 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 114 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 | C2×#102 |
| commutator | C2×C8 | C22×C4×C103 |
| Frattini, cosocle | C22×C8 | C23×C103 |
| prime radical | C103×#3169 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C2×C42×C103 ◁ C2×C4×C8×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C103×#2163 | C2 | semidirect |
| 3. C103×#1837 | C2 | semidirect |
| 4. C103×#1349 | C2 | semidirect |
| 115. #11864 | C103 | direct (N × H) |
| 122. #2163 | C2×C103 | semidirect |
| 123. #1837 | C2×C103 | semidirect |
| 124. #1349 | C2×C103 | semidirect |
| 125. C103 | #11864 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C103×#3169 | 2 |
| C103×#2163 | 2 |
| C103×#1837 | 2 |
| C103×#1349 | 2 |
| #11864 | 103 |