Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
260 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 91 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×D173 |
| commutator, socle, cosocle | C22×C173 | C24 |
| Fitting | #124×C173 | C2 |
| hypercenter | #124 | D173 |
| hypocenter | C173 | H(3,𝔽4) |
| LCS | G ▷ C22×C173 ▷ C173 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19149668 | C2 | semidirect |
| 2. #19149667 | C2 | semidirect |
| 3. #19149665 | C2 | semidirect |
| 4. #19149649 | C2 | semidirect |
| 5. #19149647 | C2 | semidirect |
| 6. #124×C173 | C2 | semidirect |
| 7. C23×D173 | C22 | semidirect |
| 8. C2×Dic346 | C22 | semidirect |
| 12. C22⋊Dic173 | C22 | semidirect |
| 13. #14583803 | C22 | semidirect |
| 14. #14583803 | C22 | semidirect |
| 15. #14583803 | C22 | semidirect |
| 16. C4×Dic173 | C22 | semidirect |
| 17. C2×Q8×C173 | C22 | semidirect |
| 19. C22⋊C4×C173 | C22 | semidirect |
| 20. C42×C173 | C22 | semidirect |
| 50. C173 | H(3,𝔽4) | semidirect |
| 55. #124 | D173 | semidirect |
| 60. C2×Q8 | C2×D173 | semidirect |
| 69. C22⋊C4 | C2×D173 | semidirect |
| 71. C42 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19149668 | 2 |
| #19149667 | 2 |
| #19149665 | 2 |
| #19149649 | 2 |
| #19149647 | 2 |
| #124×C173 | 2 |
| H(3,𝔽4) | 173 |