Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20284431 | C2 | semidirect |
| 2. #20284373 | C2 | semidirect |
| 3. C2×#16810433 | C2 | semidirect |
| 4. #20276443 | C2 | semidirect |
| 5. #20276342 | C2 | semidirect |
| 6. #20272814 | C2 | semidirect |
| 7. C53×#3414 | C2 | semidirect |
| 57. #13133153 | D4 | semidirect |
| 75. C2×Q16×C53 | D4 | semidirect |
| 79. C2×D8×C53 | D4 | semidirect |
| 87. C2×C16×C53 | D4 | semidirect |
| 220. #3414 | D53 | semidirect |
| 259. C53 | #13318 | semidirect |
| 277. C2×Q16 | C22⋊D53 | semidirect |
| 281. C2×D8 | C22⋊D53 | semidirect |
| 306. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284431 | 2 |
| #20284373 | 2 |
| C2×#16810433 | 2 |
| #20276443 | 2 |
| #20276342 | 2 |
| #20272814 | 2 |
| C53×#3414 | 2 |
| #13318 | 53 |