Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
512 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 162 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 | C2×#99 |
| commutator | C2×C4 | C2×C42×C23 |
| Frattini, cosocle | C22×Q8 | C23×C23 |
| prime radical | C22×D4×C23 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C4×Q8×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C23×#101 | C2 | semidirect |
| 4. C23×#1394 | C2 | semidirect |
| 16. C23×#355 | C4 | semidirect |
| 38. C23×#101 | C2×C4 | semidirect |
| 79. #12632 | C23 | direct (N × H) |
| 115. C4×#101 | C2×C23 | semidirect |
| 116. #1394 | C2×C23 | semidirect |
| 147. #355 | C4×C23 | semidirect |
| 175. #101 | C2×C4×C23 | semidirect |
| 181. C23 | #12632 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2326 | 2 |
| C2×C23×#355 | 2 |
| C4×C23×#101 | 2 |
| C23×#1394 | 2 |
| #12632 | 23 |