Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
224 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C2×D8 |
| commutator | C2×C8 | C22×C4×C23 |
| Frattini, cosocle | C4×C8 | C23×C23 |
| socle | C22×C23 | C4×D8 |
| prime radical | C2×D8×C23 | C2×C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C4×C8×C23 ◁ C82×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C8×Q16×C23 | C2 | semidirect |
| 4. C23×#1372 | C2 | semidirect |
| 5. C23×#1332 | C2 | semidirect |
| 7. C23×#1312 | C2 | semidirect |
| 48. Q16×C23 | M16 | semidirect |
| 68. #12071 | C23 | direct (N × H) |
| 87. C8×C23 | SD32 | semidirect |
| 92. C8×Q16 | C2×C23 | semidirect |
| 93. #1372 | C2×C23 | semidirect |
| 94. #1332 | C2×C23 | semidirect |
| 96. #1312 | C2×C23 | semidirect |
| 149. C23 | #12071 | direct (N × H) |
| 154. Q16 | M16×C23 | semidirect |
| 192. C8 | C23×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C23×SD32 | 2 |
| C23×#1589 | 2 |
| C8×Q16×C23 | 2 |
| C23×#1372 | 2 |
| C23×#1332 | 2 |
| C23×#1331 | 2 |
| C23×#1312 | 2 |
| #12071 | 23 |