Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 2. C4×#13133286 | C2 | semidirect |
| 3. #20290274 | C2 | semidirect |
| 4. #20289612 | C2 | semidirect |
| 15. Q8×#88322 | C4 | semidirect |
| 17. C8×D212 | C4 | semidirect |
| 19. #16810688 | C4 | semidirect |
| 24. C8×Q8×C53 | C4 | semidirect |
| 113. Q8×C53 | #107 | semidirect |
| 126. D212 | #107 | semidirect |
| 145. #88322 | #104 | semidirect |
| 181. C8×Q8 | #6157 | semidirect |
| 198. C53 | #8667 | semidirect |
| 284. Q8 | #13133286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290588 | 2 |
| C4×#13133286 | 2 |
| #20290274 | 2 |
| #20289612 | 2 |
| C8×#11719949 | 2 |
| #8667 | 53 |