Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
632 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20284719 | C2 | semidirect |
| 2. #20284508 | C2 | semidirect |
| 4. #20273141 | C2 | semidirect |
| 5. #20273105 | C2 | semidirect |
| 6. #20272573 | C2 | semidirect |
| 7. C53×#1518 | C2 | semidirect |
| 61. C4⋊#88322 | D4 | semidirect |
| 67. C4×#88322 | D4 | semidirect |
| 69. C4⋊Q8×C53 | D4 | semidirect |
| 70. C4⋊Q8×C53 | D4 | semidirect |
| 105. C2×D212 | SD16 | semidirect |
| 234. #1518 | D53 | semidirect |
| 270. C53 | #10000 | semidirect |
| 278. C4⋊Q8 | D212 | semidirect |
| 279. C4⋊Q8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284719 | 2 |
| #20284508 | 2 |
| #20279617 | 2 |
| #20273141 | 2 |
| #20273105 | 2 |
| #20272573 | 2 |
| C53×#1518 | 2 |
| #10000 | 53 |