Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
996 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C23 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3548 | C2 | semidirect |
| 2. C23×#3205 | C2 | semidirect |
| 3. C23×#3138 | C2 | semidirect |
| 4. C23×#1625 | C2 | semidirect |
| 5. C23×#1544 | C2 | semidirect |
| 6. C23×#1484 | C2 | semidirect |
| 10. C23×#547 | C22 | semidirect |
| 25. C23×#332 | C22 | semidirect |
| 26. C23×D4⋊C8 | C22 | semidirect |
| 104. #18727 | C23 | direct (N × H) |
| 133. #3548 | C2×C23 | semidirect |
| 134. #3205 | C2×C23 | semidirect |
| 135. #3138 | C2×C23 | semidirect |
| 136. #1625 | C2×C23 | semidirect |
| 137. #1544 | C2×C23 | semidirect |
| 138. #1484 | C2×C23 | semidirect |
| 157. #547 | C22×C23 | semidirect |
| 172. #332 | C22×C23 | semidirect |
| 173. D4⋊C8 | C22×C23 | semidirect |
| 218. C23 | #18727 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3548 | 2 |
| C23×#3205 | 2 |
| C23×#3138 | 2 |
| C23×#1625 | 2 |
| C23×#1544 | 2 |
| C23×#1484 | 2 |
| #18727 | 23 |