Finite Group DatabasebetaFinite Group DatabasebetaOrder 29988.
156 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 37 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 | #64424⋊D17 |
| commutator, hypocenter | C72×C17 | C22×C9 |
| Fitting, socle, cosocle | C3×C72×C17 | C22×C3 |
| prime radical | C3×(C7⋊D7)⋊D17 | 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⋊#11725076 | C2 | semidirect |
| 2. C17⋊#11725076 | C2 | semidirect |
| 3. C17×#11725077 | C2 | semidirect |
| 5. C17×#89204 | C22 | semidirect |
| 11. (C7⋊D7)⋊D17 | C9 | semidirect |
| 22. C17×C7⋊D7 | C2×C9 | semidirect |
| 23. C7×D119 | C2×C9 | semidirect |
| 24. C7×D119 | C2×C9 | semidirect |
| 31. #11725077 | D17 | semidirect |
| 34. C72×C17 | C22×C9 | semidirect |
| 47. #89204 | C2×D17 | semidirect |
| 60. D119 | D7⋊C9 | semidirect |
| 61. D119 | D7⋊C9 | semidirect |
| 82. C7×C17 | C2×D7⋊C9 | semidirect |
| 83. C7×C17 | C2×D7⋊C9 | semidirect |
| 87. C7⋊D7 | C9×D17 | semidirect |
| 98. C72 | C2×C9×D17 | semidirect |
| 120. C17 | #11725076⋊C2 | semidirect |
| 133. C7 | D17×D7⋊C9 | semidirect |
| 134. C7 | D17×D7⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17⋊#11725076 | 2 |
| C17×#11725077 | 2 |
| C3×(C7⋊D7)⋊D17 | 3 |
| D17×D7⋊C9 | 7 |
| #11725076⋊C2 | 17 |