Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1118 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 207 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. #20275008 | C2 | semidirect |
| 2. #20273033 | C2 | semidirect |
| 4. C23×#88322 | C22 | semidirect |
| 6. C2×C22⋊#88322 | C22 | semidirect |
| 23. H(5,𝔽2)×C53 | C8 | semidirect |
| 102. C23×C53 | C22⋊C8 | semidirect |
| 125. C2×C4×C53 | C22⋊C8 | semidirect |
| 172. C53 | #8316 | semidirect |
| 174. H(5,𝔽2) | #88322 | semidirect |
| 258. C23 | C22⋊#88322 | semidirect |
| 281. C2×C4 | C22⋊#88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275008 | 2 |
| #20273033 | 2 |
| C4×H(5,𝔽2)×C53 | 2 |
| #8316 | 53 |