Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
310 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D337 |
| commutator, socle, cosocle | C22×C337 | C24 |
| Fitting | #121×C337 | C2 |
| hypercenter | #121 | D337 |
| hypocenter | C337 | #532 |
| LCS | G ▷ C22×C337 ▷ C337 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19129184 | C2 | semidirect |
| 2. #24924958 | C2 | semidirect |
| 3. #24924955 | C2 | semidirect |
| 4. #24924945 | C2 | semidirect |
| 5. #24924933 | C2 | semidirect |
| 6. #24924931 | C2 | semidirect |
| 7. D4×Dic337 | C2 | semidirect |
| 8. #24924921 | C2 | semidirect |
| 9. #24924919 | C2 | semidirect |
| 10. C2×C4×Dic337 | C2 | semidirect |
| 11. #121×C337 | C2 | semidirect |
| 44. C2×Dic337 | D4 | semidirect |
| 71. C4×C337 | #41 | semidirect |
| 76. Dic337 | #41 | semidirect |
| 83. C337 | #532 | semidirect |
| 91. #121 | D337 | semidirect |
| 160. C4 | #19129184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19129184 | 2 |
| #24924958 | 2 |
| #24924955 | 2 |
| #24924945 | 2 |
| #24924933 | 2 |
| #24924931 | 2 |
| D4×Dic337 | 2 |
| #24924921 | 2 |
| #24924919 | 2 |
| C2×C4×Dic337 | 2 |
| #121×C337 | 2 |
| #532 | 337 |