Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
160 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #2226 |
| commutator, Frattini, cosocle | C2×C16 | C23×C23 |
| prime radical | C23×#508 | C22 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C4×C8×C23 ◁ C4×C16×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#2254 | C2 | semidirect |
| 3. C23×#1426 | C2 | semidirect |
| 4. C23×#1422 | C2 | semidirect |
| 18. C23×Q32 | Q8 | semidirect |
| 20. C23×D16 | Q8 | semidirect |
| 45. #13710 | C23 | direct (N × H) |
| 59. #2254 | C2×C23 | semidirect |
| 61. #1426 | C2×C23 | semidirect |
| 62. #1422 | C2×C23 | semidirect |
| 86. Q32 | Q8×C23 | semidirect |
| 88. D16 | Q8×C23 | semidirect |
| 97. C23 | #13710 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2254 | 2 |
| C23×#2178 | 2 |
| C23×#1426 | 2 |
| C23×#1422 | 2 |
| C23×#1418 | 2 |
| #13710 | 23 |