Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
234 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #442 |
| commutator | C2×C8 | C22×C4×C23 |
| Frattini, cosocle | C4×C8 | C23×C23 |
| prime radical | C2×C23×D16 | C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ C23×#322 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1594 | C2 | semidirect |
| 3. C23×#1580 | C2 | semidirect |
| 4. C23×#1368 | C2 | semidirect |
| 5. C23×#1333 | C2 | semidirect |
| 6. C23×#1333 | C2 | semidirect |
| 7. C23×#1313 | C2 | semidirect |
| 51. D8×C23 | M16 | semidirect |
| 68. #12078 | C23 | direct (N × H) |
| 92. #1594 | C2×C23 | semidirect |
| 93. #1580 | C2×C23 | semidirect |
| 94. #1368 | C2×C23 | semidirect |
| 95. #1333 | C2×C23 | semidirect |
| 96. #1333 | C2×C23 | semidirect |
| 97. #1313 | C2×C23 | semidirect |
| 152. C23 | #12078 | direct (N × H) |
| 160. D8 | M16×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2177 | 2 |
| C23×#1594 | 2 |
| C23×#1580 | 2 |
| C23×#1368 | 2 |
| C23×#1333 | 2 |
| C23×#1313 | 2 |
| #12078 | 23 |