Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
522 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #401×C71 | C2 | semidirect |
| 2. #397×C71 | C2 | semidirect |
| 3. #396×C71 | C2 | semidirect |
| 4. #394×C71 | C2 | semidirect |
| 5. #392×C71 | C2 | semidirect |
| 6. #392×C71 | C2 | semidirect |
| 7. #386×C71 | C2 | semidirect |
| 89. #2825 | C71 | direct (N × H) |
| 90. C71 | #2825 | direct (N × H) |
| 91. #401 | C2×C71 | semidirect |
| 92. #397 | C2×C71 | semidirect |
| 93. #396 | C2×C71 | semidirect |
| 94. #394 | C2×C71 | semidirect |
| 95. #392 | C2×C71 | semidirect |
| 96. #392 | C2×C71 | semidirect |
| 97. #386 | C2×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #401×C71 | 2 |
| #397×C71 | 2 |
| #396×C71 | 2 |
| #394×C71 | 2 |
| #392×C71 | 2 |
| #386×C71 | 2 |
| #2825 | 71 |