Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C53 |
| prime radical | C53×#2246 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ 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 |
|---|---|---|
| 1. C53×#2254 | C2 | semidirect |
| 3. C53×#2240 | C2 | semidirect |
| 4. C53×#1706 | C2 | semidirect |
| 5. C53×#1311 | C2 | semidirect |
| 43. C16×C53 | SD16 | semidirect |
| 56. #12506 | C53 | direct (N × H) |
| 65. #2254 | C2×C53 | semidirect |
| 67. #2240 | C2×C53 | semidirect |
| 68. #1706 | C2×C53 | semidirect |
| 69. #1311 | C2×C53 | semidirect |
| 83. C53 | #12506 | direct (N × H) |
| 111. C16 | SD16×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2254 | 2 |
| C53×#2246 | 2 |
| C53×#2240 | 2 |
| C53×#1706 | 2 |
| C53×#1311 | 2 |
| #12506 | 53 |