Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #466 |
| commutator, Frattini, cosocle | C4×C8 | C23×C23 |
| prime radical | C23×#1667 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ C8×D4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#2248 | C2 | semidirect |
| 2. D4×C16×C23 | C2 | semidirect |
| 3. C23×#1669 | C2 | semidirect |
| 5. C23×#1372 | C2 | semidirect |
| 6. C23×#1362 | C2 | semidirect |
| 7. C23×#1361 | C2 | semidirect |
| 73. C16×C23 | D8 | semidirect |
| 74. #12432 | C23 | direct (N × H) |
| 85. D4×C23 | SD32 | semidirect |
| 99. #2248 | C2×C23 | semidirect |
| 100. D4×C16 | C2×C23 | semidirect |
| 101. #1669 | C2×C23 | semidirect |
| 103. #1372 | C2×C23 | semidirect |
| 104. #1362 | C2×C23 | semidirect |
| 105. #1361 | C2×C23 | semidirect |
| 163. C23 | #12432 | direct (N × H) |
| 191. C16 | D8×C23 | semidirect |
| 202. D4 | C23×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2248 | 2 |
| D4×C16×C23 | 2 |
| C23×#1669 | 2 |
| C23×#1667 | 2 |
| C23×#1372 | 2 |
| C23×#1362 | 2 |
| C23×#1361 | 2 |
| #12432 | 23 |