Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
708 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C241 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C241 |
| prime radical | C2×#121×C241 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C241 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#123×C241 | C2 | semidirect |
| 3. C22×C4⋊C4×C241 | C2 | semidirect |
| 4. #399×C241 | C2 | semidirect |
| 5. #390×C241 | C2 | semidirect |
| 6. #384×C241 | C2 | semidirect |
| 7. C4×C22⋊C4×C241 | C2 | semidirect |
| 45. C22⋊C4×C241 | D4 | semidirect |
| 87. C4×C241 | #123 | semidirect |
| 94. C241 | #2501 | direct (N × H) |
| 95. #2501 | C241 | direct (N × H) |
| 96. C2×#123 | C2×C241 | semidirect |
| 98. C22×C4⋊C4 | C2×C241 | semidirect |
| 99. #399 | C2×C241 | semidirect |
| 100. #390 | C2×C241 | semidirect |
| 101. #384 | C2×C241 | semidirect |
| 102. C4×C22⋊C4 | C2×C241 | semidirect |
| 140. C22⋊C4 | D4×C241 | semidirect |
| 182. C4 | #123×C241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#123×C241 | 2 |
| C2×#121×C241 | 2 |
| C22×C4⋊C4×C241 | 2 |
| #399×C241 | 2 |
| #390×C241 | 2 |
| #384×C241 | 2 |
| C4×C22⋊C4×C241 | 2 |
| #2501 | 241 |