Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
118 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #1333 |
| commutator | C16 | C2×C8×C23 |
| Frattini, cosocle | #346 | C22×C23 |
| prime radical | C23×#508 | C4 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C4×C8×C23 ◁ C23×#346 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1398 | C2 | semidirect |
| 3. C23×#1368 | C2 | semidirect |
| 13. C23×Q32 | C8 | semidirect |
| 15. C23×D16 | C8 | semidirect |
| 37. #7389 | C23 | direct (N × H) |
| 50. #1398 | C2×C23 | semidirect |
| 51. #1368 | C2×C23 | semidirect |
| 70. Q32 | C8×C23 | semidirect |
| 72. D16 | C8×C23 | semidirect |
| 80. C23 | #7389 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2179 | 2 |
| C23×#1398 | 2 |
| C23×#1368 | 2 |
| #7389 | 23 |