Finite Group DatabasebetaFinite Group DatabasebetaOrder 29988.
146 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 19 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×C17×#3862 | C22 |
| Fitting, socle | C3×C72×C17 | C2×D3 |
| LCS | G ▷ C3×C17×#3862 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×C3⋊#64418 | C2 | semidirect |
| 2. C3⋊(C17⋊#64425) | C2 | semidirect |
| 3. C3×C17⋊#64418 | C2 | semidirect |
| 6. C3×C17×#3862 | C22 | semidirect |
| 7. C3⋊(C7⋊D119) | D3 | semidirect |
| 10. C17⋊#64418 | D3 | semidirect |
| 16. C17×#3862 | C2×D3 | semidirect |
| 17. C3×C72×C17 | C2×D3 | semidirect |
| 27. C3⋊#64418 | D17 | semidirect |
| 29. C72×C17 | D32 | semidirect |
| 43. C3×#3862 | C2×D17 | semidirect |
| 70. C3×C72 | D3×D17 | semidirect |
| 72. #3862 | D3×D17 | semidirect |
| 93. C3×C17 | #64418⋊C2 | semidirect |
| 94. C72 | (C3⋊D3)⋊D17 | semidirect |
| 117. C17 | #64418⋊D3 | semidirect |
| 141. C3 | #64418⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×C3⋊#64418 | 2 |
| C3⋊(C17⋊#64425) | 2 |
| C3×C17⋊#64418 | 2 |
| D21×D119 | 3 |
| #64418⋊D17 | 3 |
| #64418⋊D3 | 17 |
| (C3⋊D3)⋊D17 | 49 |