Finite Group DatabasebetaFinite Group DatabasebetaOrder 29888.
292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 113 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×D467 |
| commutator, socle, cosocle | C22×C467 | C24 |
| Fitting | C2×#41×C467 | C2 |
| hypercenter | C2×#41 | D467 |
| hypocenter | C467 | #547 |
| LCS | G ▷ C22×C467 ▷ C467 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#21418742 | C2 | semidirect |
| 2. #28417951 | C2 | semidirect |
| 3. #28417936 | C2 | semidirect |
| 4. #28417934 | C2 | semidirect |
| 5. #28417932 | C2 | semidirect |
| 6. #28417929 | C2 | semidirect |
| 7. #28417925 | C2 | semidirect |
| 8. D4×Dic467 | C2 | semidirect |
| 9. C4×C22⋊D467 | C2 | semidirect |
| 10. C2×Dic467⋊C4 | C2 | semidirect |
| 11. C2×#41×C467 | C2 | semidirect |
| 53. D4×C467 | D4 | semidirect |
| 76. Dic467 | #41 | semidirect |
| 83. C467 | #547 | semidirect |
| 86. C2×#41 | D467 | semidirect |
| 129. D4 | C22⋊D467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21418742 | 2 |
| #28417951 | 2 |
| #28417936 | 2 |
| #28417934 | 2 |
| #28417932 | 2 |
| #28417929 | 2 |
| #28417925 | 2 |
| D4×Dic467 | 2 |
| C4×C22⋊D467 | 2 |
| C2×Dic467⋊C4 | 2 |
| C2×#41×C467 | 2 |
| #547 | 467 |