Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
772 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 138 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×C23 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C23 |
| prime radical | C23×#2656 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C23×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C23×#481 | C2 | semidirect |
| 3. C2×C23×#327 | C2 | semidirect |
| 4. C23×#1445 | C2 | semidirect |
| 5. C23×#1280 | C2 | semidirect |
| 39. C2×C4⋊C4×C23 | D4 | semidirect |
| 45. C23×C22⋊C8 | D4 | semidirect |
| 92. #9968 | C23 | direct (N × H) |
| 136. C2×#481 | C2×C23 | semidirect |
| 138. C2×#327 | C2×C23 | semidirect |
| 139. #1445 | C2×C23 | semidirect |
| 140. #1280 | C2×C23 | semidirect |
| 210. C2×C4⋊C4 | D4×C23 | semidirect |
| 216. C22⋊C8 | D4×C23 | semidirect |
| 220. C23 | #9968 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#481 | 2 |
| C23×#2656 | 2 |
| C2×C23×#327 | 2 |
| C23×#1445 | 2 |
| C23×#1280 | 2 |
| #9968 | 23 |