Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
948 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator, socle | C23×C47 | C24 |
| Fitting | C47×#392 | C2 |
| hypercenter | #392 | D47 |
| hypocenter | C47 | #2541 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13094020 | C2 | semidirect |
| 2. C2×#13094020 | C2 | semidirect |
| 3. C2×#13093997 | C2 | semidirect |
| 4. C2×#13093996 | C2 | semidirect |
| 5. C2×(C22⋊D47)⋊C4 | C2 | semidirect |
| 6. #15689033 | C2 | semidirect |
| 7. #15689032 | C2 | semidirect |
| 8. #15689031 | C2 | semidirect |
| 9. #15689023 | C2 | semidirect |
| 10. #15688974 | C2 | semidirect |
| 11. C47×#392 | C2 | semidirect |
| 66. C2×C22⋊D47 | D4 | semidirect |
| 87. Dic47⋊C4 | D4 | semidirect |
| 89. C4×Dic47 | D4 | semidirect |
| 177. Dic47 | #121 | semidirect |
| 178. Dic47 | #127 | semidirect |
| 197. #392 | D47 | semidirect |
| 200. C47 | #2541 | semidirect |