Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
500 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 134 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 | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×Q8 | C23×C23 |
| prime radical | C22×D4×C23 | C2×C4 |
| LCS | G ▷ C22×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. C23×#1801 | C2 | semidirect |
| 4. C23×#1394 | C2 | semidirect |
| 87. #12801 | C23 | direct (N × H) |
| 127. #1801 | C2×C23 | semidirect |
| 128. #1394 | C2×C23 | semidirect |
| 149. C4×C23 | #355 | semidirect |
| 198. C23 | #12801 | direct (N × H) |
| 296. C4 | C23×#355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C23×#124 | 2 |
| C2×C23×#355 | 2 |
| C23×#1801 | 2 |
| C23×#1394 | 2 |
| #12801 | 23 |