Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
262 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #1390 |
| commutator | C2×Q8 | C42×C53 |
| Frattini, cosocle | C2×C4⋊Q8 | C22×C53 |
| prime radical | C23×C53 | #99 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C23×C53 ◁ C22×C4×C53 ◁ C2×C4⋊Q8×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C53×#356 | C4 | semidirect |
| 14. C53×#333 | C4 | semidirect |
| 95. #7483 | C53 | direct (N × H) |
| 123. #356 | C4×C53 | semidirect |
| 126. #333 | C4×C53 | semidirect |
| 127. C53 | #7483 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C53×#356 | 2 |
| C53×#1886 | 2 |
| C53×#1558 | 2 |
| #7483 | 53 |