Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
304 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 46 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 | #353 |
| commutator | C2×C42 | C2×C4×C53 |
| Frattini, cosocle | #391 | C22×C53 |
| prime radical | C2×#127×C53 | C4 |
| LCS | G ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C23×C53 ◁ C22×C4×C53 ◁ C53×#391 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#1394 | C2 | semidirect |
| 3. C53×#1319 | C2 | semidirect |
| 90. #7404 | C53 | direct (N × H) |
| 108. #1394 | C2×C53 | semidirect |
| 109. #1319 | C2×C53 | semidirect |
| 123. C53 | #7404 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2014 | 2 |
| C53×#1394 | 2 |
| C53×#1319 | 2 |
| #7404 | 53 |