Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
514 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. #20283351 | C2 | semidirect |
| 3. #20273158 | C2 | semidirect |
| 4. #20273047 | C2 | semidirect |
| 5. #20272581 | C2 | semidirect |
| 6. #20272580 | C2 | semidirect |
| 7. C53×#1490 | C2 | semidirect |
| 54. C4×#88322 | D4 | semidirect |
| 75. C4×C8×C53 | D4 | semidirect |
| 217. #1490 | D53 | semidirect |
| 251. C53 | #9494 | semidirect |
| 290. C4×C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283351 | 2 |
| #20280275 | 2 |
| #20273158 | 2 |
| #20273047 | 2 |
| #20272581 | 2 |
| #20272580 | 2 |
| C53×#1490 | 2 |
| #9494 | 53 |