Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
474 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C23 |
| prime radical | C23×C23 | #121 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 55. C2×Q8×C23 | Q16 | semidirect |
| 84. #10259 | C23 | direct (N × H) |
| 180. C23 | #10259 | direct (N × H) |
| 186. C2×Q8 | Q16×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3249 | 2 |
| C23×#3078 | 2 |
| C23×#1984 | 2 |
| C23×#1493 | 2 |
| C23×#1292 | 2 |
| #10259 | 23 |