Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
258 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 258 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 | C22×C23 | C4×D8 |
| prime radical | C2×C23×D16 | C4 |
| 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 |
|---|---|---|
| 2. C8×D8×C23 | C2 | semidirect |
| 3. C23×#1371 | C2 | semidirect |
| 4. C23×#1331 | C2 | semidirect |
| 5. C8×C16×C23 | C2 | semidirect |
| 19. C23×D16 | C8 | direct (N × H) |
| 33. D8×C23 | C2×C8 | semidirect |
| 46. C16×C23 | C2×C8 | semidirect |
| 47. C8×D16 | C23 | direct (N × H) |
| 61. C8×C23 | D16 | direct (N × H) |
| 65. C8×D8 | C2×C23 | semidirect |
| 66. #1371 | C2×C23 | semidirect |
| 67. #1331 | C2×C23 | semidirect |
| 68. C8×C16 | C2×C23 | semidirect |
| 96. D16 | C8×C23 | direct (N × H) |
| 107. C23 | C8×D16 | direct (N × H) |
| 111. D8 | C2×C8×C23 | semidirect |
| 124. C16 | C2×C8×C23 | semidirect |
| 138. C8 | C23×D16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C23×D16 | 2 |
| C8×D8×C23 | 2 |
| C23×#1371 | 2 |
| C23×#1331 | 2 |
| C8×C16×C23 | 2 |
| C8×D16 | 23 |