Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C53 | C22⋊C4 |
| commutator | C2×C4 | C2×C42×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| socle, prime radical | C23×C53 | C2×C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C53 ◁ C43×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. C53×#330 | C4 | direct (N × H) |
| 80. C4×#330 | C53 | direct (N × H) |
| 93. C4×C53 | #330 | direct (N × H) |
| 113. #330 | C4×C53 | direct (N × H) |
| 114. C53 | C4×#330 | direct (N × H) |
| 191. C4 | C53×#330 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#125×C53 | 2 |
| C4×#97×C53 | 2 |
| C2×C53×#330 | 2 |
| C53×#1295 | 2 |
| C4×#330 | 53 |