Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
226 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C23 | D8 |
| commutator | C8 | C22×C8×C23 |
| Frattini, cosocle | C4×C8 | C23×C23 |
| socle, prime radical | C22×C23 | C4×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C23 ◁ C4×C8×C23 ◁ C82×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 18. C23×Q32 | C8 | direct (N × H) |
| 46. C8×Q32 | C23 | direct (N × H) |
| 58. C8×C23 | Q32 | direct (N × H) |
| 89. Q32 | C8×C23 | direct (N × H) |
| 101. C23 | C8×Q32 | direct (N × H) |
| 129. C8 | C23×Q32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C23×Q32 | 2 |
| C8×Q16×C23 | 2 |
| C23×#1371 | 2 |
| C23×#1332 | 2 |
| C8×C16×C23 | 2 |
| C8×Q32 | 23 |