Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
658 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #95 |
| commutator | C23 | C2×C42×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C24×C53 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C22×C42×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#1309 | C2 | direct (N × H) |
| 58. C2×#1309 | C53 | direct (N × H) |
| 70. #1309 | C2×C53 | direct (N × H) |
| 73. C2×C53 | #1309 | direct (N × H) |
| 81. C53 | C2×#1309 | direct (N × H) |
| 143. C2 | C53×#1309 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C53×#423 | 2 |
| C53×#1309 | 2 |
| C2×#1309 | 53 |