Finite Group DatabasebetaFinite Group DatabasebetaOrder 29988.
128 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 39 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 | C3 | #64422⋊D17 |
| commutator, hypocenter | C72×C17 | C22×C9 |
| Fitting, socle, cosocle | C3×C72×C17 | C22×C3 |
| prime radical | C3×D7×D119 | C3 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17⋊#11725075 | C2 | semidirect |
| 2. C17×#11725075 | C2 | semidirect |
| 3. C17⋊#11725078 | C2 | semidirect |
| 5. C17×#89205 | C22 | semidirect |
| 11. D7×D119 | C9 | semidirect |
| 20. C7⋊D119 | C2×C9 | semidirect |
| 21. C7×D119 | C2×C9 | semidirect |
| 22. C7×D7×C17 | C2×C9 | semidirect |
| 29. #11725075 | D17 | semidirect |
| 30. C72×C17 | C22×C9 | semidirect |
| 42. #89205 | C2×D17 | semidirect |
| 58. D119 | D7⋊C9 | semidirect |
| 60. D7×C17 | D7⋊C9 | semidirect |
| 72. C7×C17 | C2×D7⋊C9 | semidirect |
| 73. C7×C17 | C2×D7⋊C9 | semidirect |
| 79. C7×D7 | C9×D17 | semidirect |
| 86. C72 | C2×C9×D17 | semidirect |
| 106. C17 | #11725075⋊C2 | semidirect |
| 113. D7 | C17⋊(D7⋊C9) | semidirect |
| 117. C7 | D17×D7⋊C9 | semidirect |
| 118. C7 | C2×C17⋊(D7⋊C9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17⋊#11725075 | 2 |
| C17×#11725075 | 2 |
| C17⋊#11725078 | 2 |
| C3×D7×D119 | 3 |
| C2×C17⋊(D7⋊C9) | 7 |
| D17×D7⋊C9 | 7 |
| #11725075⋊C2 | 17 |