Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
662 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20285183 | C2 | semidirect |
| 2. #20280567 | C2 | semidirect |
| 3. #20273338 | C2 | semidirect |
| 4. #20273262 | C2 | semidirect |
| 5. #20273158 | C2 | semidirect |
| 6. #20272581 | C2 | semidirect |
| 7. C53×#3109 | C2 | semidirect |
| 55. C4×#88322 | D4 | semidirect |
| 64. C4⋊Q8×C53 | D4 | semidirect |
| 65. #127×C53 | D4 | semidirect |
| 83. #97×C53 | D4 | semidirect |
| 222. #3109 | D53 | semidirect |
| 260. C53 | #10018 | semidirect |
| 275. C4⋊Q8 | C22⋊D53 | semidirect |
| 276. #127 | C22⋊D53 | semidirect |
| 306. #97 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285183 | 2 |
| #20280567 | 2 |
| #20273338 | 2 |
| #20273262 | 2 |
| #20273158 | 2 |
| #20272581 | 2 |
| C53×#3109 | 2 |
| #10018 | 53 |