Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
444 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 200 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×C71 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C71 |
| prime radical | C24×C71 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #391×C71 | C2 | semidirect |
| 4. #387×C71 | C2 | semidirect |
| 26. C22×C4×C71 | Q8 | semidirect |
| 77. #2607 | C71 | direct (N × H) |
| 78. C71 | #2607 | direct (N × H) |
| 81. #391 | C2×C71 | semidirect |
| 82. #387 | C2×C71 | semidirect |
| 104. C22×C4 | Q8×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #399×C71 | 2 |
| #393×C71 | 2 |
| #391×C71 | 2 |
| #387×C71 | 2 |
| #381×C71 | 2 |
| C4×C22⋊C4×C71 | 2 |
| #2607 | 71 |