Finite Group DatabasebetaFinite Group DatabasebetaOrder 17100.
128 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C19×C52⋊C3 | C22 |
| Fitting, socle | C3×C52×C19 | C2×D3 |
| LCS | G ▷ C3×C19×C52⋊C3 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52⋊C3×D57 | C2 | semidirect |
| 2. C3⋊(C19⋊#3874) | C2 | semidirect |
| 3. C3×C19×#3874 | C2 | semidirect |
| 6. C3×C19×C52⋊C3 | C22 | semidirect |
| 8. C52×D57 | D3 | semidirect |
| 13. C19×#3874 | D3 | semidirect |
| 15. C3×C52×C19 | C2×D3 | semidirect |
| 17. C19×C52⋊C3 | C2×D3 | semidirect |
| 31. C52×C19 | D32 | semidirect |
| 34. C3×#3874 | D19 | semidirect |
| 46. C3×C52⋊C3 | C2×D19 | semidirect |
| 60. #3874 | D57 | direct (N × H) |
| 65. D57 | #3874 | direct (N × H) |
| 72. C3×C52 | D3×D19 | semidirect |
| 74. C52⋊C3 | C2×D57 | semidirect |
| 79. C3×C19 | C2×#3874 | semidirect |
| 93. C52 | D3×D57 | semidirect |
| 96. C19 | D3×#3874 | semidirect |
| 123. C3 | D19×#3874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52⋊C3×D57 | 2 |
| C3⋊(C19⋊#3874) | 2 |
| C3×C19×#3874 | 2 |
| C5×D5×D57 | 3 |
| D19×#3874 | 3 |
| D3×#3874 | 19 |
| D3×D57 | 25 |