Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C53 | #331 |
| commutator | C4×C8 | C2×C4×C53 |
| Frattini, cosocle | C82 | C22×C53 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C42×C53 ◁ C82×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 53. #7095 | C53 | direct (N × H) |
| 75. C53 | #7095 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#1707 | 2 |
| C53×#1370 | 2 |
| C53×#1367 | 2 |
| #7095 | 53 |