Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
882 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 238 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 | C42 | C24×C23 |
| prime radical | C2×C23×#127 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C23×#564 | C2 | semidirect |
| 3. C23×#1658 | C2 | direct (N × H) |
| 4. C2×C23×#330 | C2 | semidirect |
| 6. C23×#564 | C22 | semidirect |
| 14. C23×#330 | C22 | semidirect |
| 48. C2×#1658 | C23 | direct (N × H) |
| 60. C2×#564 | C2×C23 | semidirect |
| 62. #1658 | C2×C23 | direct (N × H) |
| 63. C2×#330 | C2×C23 | semidirect |
| 72. #564 | C22×C23 | semidirect |
| 80. #330 | C22×C23 | semidirect |
| 82. C2×C23 | #1658 | direct (N × H) |
| 101. C23 | C2×#1658 | direct (N × H) |
| 137. C2 | C23×#1658 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#564 | 2 |
| C2×C23×#490 | 2 |
| C23×#1658 | 2 |
| C2×C23×#330 | 2 |
| C2×#1658 | 23 |