Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 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×D293 |
| commutator, socle, cosocle | C22×C293 | C24 |
| Fitting | #124×C293 | C2 |
| prime radical | #22627592 | C2 |
| hypercenter | #124 | D293 |
| hypocenter | C293 | #551 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22627617 | C2 | semidirect |
| 2. #22627606 | C2 | semidirect |
| 3. #22627605 | C2 | semidirect |
| 4. #22627600 | C2 | semidirect |
| 6. #22627584 | C2 | semidirect |
| 7. #22627581 | C2 | semidirect |
| 8. C22⋊C4×D293 | C2 | semidirect |
| 9. #124×C293 | C2 | semidirect |
| 12. C22×Dic293 | C22 | semidirect |
| 15. C4⋊Dic293 | C22 | semidirect |
| 16. #17989781 | C22 | semidirect |
| 17. #17989781 | C22 | semidirect |
| 18. #17989781 | C22 | semidirect |
| 21. C22⋊Dic293 | C22 | semidirect |
| 25. C4×Dic293 | C22 | semidirect |
| 26. C2×Q8×C293 | C22 | semidirect |
| 29. C22⋊C4×C293 | C22 | semidirect |
| 30. C42×C293 | C22 | semidirect |
| 68. C293 | #551 | semidirect |
| 71. #124 | D293 | semidirect |
| 80. C2×Q8 | C2×D293 | semidirect |
| 97. C22⋊C4 | C2×D293 | semidirect |
| 99. C42 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627617 | 2 |
| #22627606 | 2 |
| #22627605 | 2 |
| #22627600 | 2 |
| #22627592 | 2 |
| #22627584 | 2 |
| #22627581 | 2 |
| C22⋊C4×D293 | 2 |
| #124×C293 | 2 |
| #551 | 293 |