Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
330 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D293 |
| commutator, socle, cosocle | C22×C293 | C24 |
| Frattini | C22 | C23×D293 |
| Fitting | #117×C293 | C2 |
| hypercenter | #117 | D293 |
| hypocenter | C293 | #525 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17989802 | C2 | semidirect |
| 2. C22×C4×D293 | C2 | semidirect |
| 3. #22627608 | C2 | semidirect |
| 4. #22627604 | C2 | semidirect |
| 5. #22627599 | C2 | semidirect |
| 6. #22627594 | C2 | semidirect |
| 7. C4×D1172 | C2 | semidirect |
| 8. #117×C293 | C2 | semidirect |
| 11. C2×Dic586 | C22 | semidirect |
| 13. C2×D1172 | C22 | semidirect |
| 19. C2×C4×D293 | C22 | semidirect |
| 20. C4⋊Dic293 | C22 | semidirect |
| 22. #17989779 | C22 | semidirect |
| 24. C4⋊C4×C293 | C22 | semidirect |
| 26. C42×C293 | C22 | semidirect |
| 42. C2×C4×C293 | D4 | semidirect |
| 54. C2×D293 | #41 | semidirect |
| 65. C293 | #525 | semidirect |
| 74. #117 | D293 | semidirect |
| 88. C4⋊C4 | C2×D293 | semidirect |
| 92. C42 | C2×D293 | semidirect |
| 108. C2×C4 | D1172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989802 | 2 |
| C22×C4×D293 | 2 |
| #22627608 | 2 |
| #22627604 | 2 |
| #22627599 | 2 |
| #22627594 | 2 |
| C4×D1172 | 2 |
| #117×C293 | 2 |
| #525 | 293 |