Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
648 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C53×#2819 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C53×#497 | C2 | semidirect |
| 2. C2×C53×#489 | C2 | semidirect |
| 4. C53×#1993 | C2 | semidirect |
| 5. C2×C53×#329 | C2 | semidirect |
| 6. C2×C53×#329 | C2 | semidirect |
| 7. C53×#1295 | C2 | semidirect |
| 47. C4⋊Q8×C53 | D4 | semidirect |
| 72. #97×C53 | D4 | semidirect |
| 73. #97×C53 | D4 | semidirect |
| 178. #10081 | C53 | direct (N × H) |
| 204. C2×#497 | C2×C53 | semidirect |
| 205. C2×#489 | C2×C53 | semidirect |
| 207. #1993 | C2×C53 | semidirect |
| 208. C2×#329 | C2×C53 | semidirect |
| 209. C2×#329 | C2×C53 | semidirect |
| 210. #1295 | C2×C53 | semidirect |
| 241. C53 | #10081 | direct (N × H) |
| 258. C4⋊Q8 | D4×C53 | semidirect |
| 283. #97 | D4×C53 | semidirect |
| 284. #97 | D4×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C53×#497 | 2 |
| C2×C53×#489 | 2 |
| C53×#2819 | 2 |
| C53×#1993 | 2 |
| C2×C53×#329 | 2 |
| C53×#1295 | 2 |
| #10081 | 53 |