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. #20284802 | C2 | semidirect |
| 2. #20280568 | C2 | semidirect |
| 3. #20273339 | C2 | semidirect |
| 4. #20273262 | C2 | semidirect |
| 5. #20273159 | C2 | semidirect |
| 6. #20272580 | C2 | semidirect |
| 7. C53×#3153 | C2 | semidirect |
| 53. #13133128 | D4 | semidirect |
| 68. C4⋊Q8×C53 | D4 | semidirect |
| 69. #127×C53 | D4 | semidirect |
| 83. C4×C8×C53 | D4 | semidirect |
| 221. #3153 | D53 | semidirect |
| 260. C53 | #10018 | semidirect |
| 275. C4⋊Q8 | C22⋊D53 | semidirect |
| 276. #127 | C22⋊D53 | semidirect |
| 307. C4×C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284802 | 2 |
| #20280568 | 2 |
| #20273339 | 2 |
| #20273262 | 2 |
| #20273159 | 2 |
| #20272580 | 2 |
| C53×#3153 | 2 |
| #10018 | 53 |