Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
726 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20289641 | C2 | direct (N × H) |
| 36. C23×C4×C53 | C8 | semidirect |
| 62. C22×C4×C53 | C2×C8 | semidirect |
| 158. C2×C53 | #1317 | semidirect |
| 171. C53 | C2×#1317 | semidirect |
| 181. C23×C4 | #88324 | semidirect |
| 228. C22×C4 | C2×#88324 | semidirect |
| 312. C2 | #20289641 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811466 | 2 |
| #20289641 | 2 |
| C2×#16810486 | 2 |
| C2×#1317 | 53 |