Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
256 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 78 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×C53 | #342 |
| commutator | C22×C4 | C42×C53 |
| Frattini, cosocle | C2×C4×Q8 | C22×C53 |
| prime radical | C23×C53 | #95 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×C4×Q8×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 91. #7323 | C53 | direct (N × H) |
| 126. C53 | #7323 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#1985 | 2 |
| C53×#1801 | 2 |
| C53×#1467 | 2 |
| #7323 | 53 |