Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
802 conjugacy classes of subgroups; only the 379 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 379 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. #20273014 | C2 | direct (N × H) |
| 3. C2×#16810345 | C2 | semidirect |
| 4. C2×C82×C53 | C2 | semidirect |
| 11. #16810345 | C22 | semidirect |
| 13. C82×C53 | C22 | semidirect |
| 64. C2×C82 | D53 | semidirect |
| 65. C2×C53 | #1454 | semidirect |
| 76. C82 | C2×D53 | semidirect |
| 77. C53 | C2×#1454 | semidirect |
| 125. C2 | #20273014 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810674 | 2 |
| #20273014 | 2 |
| C2×#16810345 | 2 |
| C2×C82×C53 | 2 |
| C2×#1454 | 53 |