Finite Group DatabasebetaFinite Group DatabasebetaOrder 16380.
120 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C7×C9×C13 | C22 |
| Frattini | C3 | D15×D91 |
| socle | C3×C5×C7×C13 | C2×D3 |
| LCS | G ▷ C5×C7×C9×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4095 | C2 | semidirect |
| 2. C7×C13×D45 | C2 | semidirect |
| 3. C5×C9×D91 | C2 | semidirect |
| 5. C5×C7×C9×C13 | C22 | semidirect |
| 14. C9×D91 | D5 | semidirect |
| 18. C13×D45 | D7 | semidirect |
| 23. C5×D91 | D9 | semidirect |
| 24. C7×C9×C13 | C2×D5 | semidirect |
| 27. C7×D45 | D13 | semidirect |
| 29. C5×C9×C13 | C2×D7 | semidirect |
| 34. C5×C7×C13 | C2×D9 | semidirect |
| 40. C5×C7×C9 | C2×D13 | semidirect |
| 53. D91 | D45 | direct (N × H) |
| 63. C9×C13 | D5×D7 | semidirect |
| 65. C7×C13 | C2×D45 | semidirect |
| 68. D45 | D91 | direct (N × H) |
| 76. C5×C13 | D7×D9 | semidirect |
| 77. C7×C9 | D5×D13 | semidirect |
| 80. C5×C9 | C2×D91 | semidirect |
| 86. C5×C7 | D9×D13 | semidirect |
| 103. C13 | D7×D45 | semidirect |
| 108. C9 | D5×D91 | semidirect |
| 109. C7 | D13×D45 | semidirect |
| 113. C5 | D9×D91 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4095 | 2 |
| C7×C13×D45 | 2 |
| C5×C9×D91 | 2 |
| D15×D91 | 3 |
| D9×D91 | 5 |
| D13×D45 | 7 |
| D7×D45 | 13 |