Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
1058 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 451 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 | C24×D103 |
| commutator, socle, cosocle | C22×C103 | C25 |
| Fitting | H(3,𝔽4)×C103 | C2 |
| hypercenter | H(3,𝔽4) | D103 |
| hypocenter | C103 | #3529 |
| LCS | G ▷ C22×C103 ▷ C103 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20268541 | C2 | semidirect |
| 2. #20268535 | C2 | semidirect |
| 3. #20268530 | C2 | semidirect |
| 4. #20268340 | C2 | semidirect |
| 5. #20268320 | C2 | semidirect |
| 6. #20268297 | C2 | semidirect |
| 7. H(3,𝔽4)×C103 | C2 | semidirect |
| 8. C2×#13110106 | C22 | semidirect |
| 10. C23×Dic103 | C22 | semidirect |
| 11. #15693019 | C22 | semidirect |
| 13. #15693014 | C22 | semidirect |
| 14. #15693013 | C22 | semidirect |
| 15. #15693009 | C22 | semidirect |
| 16. #15693005 | C22 | semidirect |
| 17. #15693003 | C22 | semidirect |
| 19. #15692998 | C22 | semidirect |
| 20. #15692997 | C22 | semidirect |
| 21. #15692994 | C22 | semidirect |
| 24. #15692990 | C22 | semidirect |
| 25. Q8×Dic103 | C22 | semidirect |
| 27. (C22⋊D103)⋊C4 | C22 | semidirect |
| 28. #15692977 | C22 | semidirect |
| 29. C42×D103 | C22 | semidirect |
| 98. C103 | #3529 | semidirect |
| 101. H(3,𝔽4) | D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268541 | 2 |
| #20268535 | 2 |
| #20268530 | 2 |
| #20268340 | 2 |
| #20268320 | 2 |
| #20268297 | 2 |
| H(3,𝔽4)×C103 | 2 |
| #3529 | 103 |