Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
194 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #2177 |
| commutator | C16 | C22×C4×C23 |
| Frattini, cosocle | C2×C16 | C23×C23 |
| prime radical | C23×#2263 | C2 |
| 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×#2179 | C2 | semidirect |
| 3. C23×#2177 | C2 | semidirect |
| 4. C23×#1426 | C2 | semidirect |
| 5. C23×#1419 | C2 | semidirect |
| 6. C23×#1418 | C2 | semidirect |
| 7. C23×#1398 | C2 | semidirect |
| 12. C23×SD64 | C4 | semidirect |
| 13. C23×D32 | C4 | semidirect |
| 25. C23×Q32 | C2×C4 | semidirect |
| 29. C23×D16 | C2×C4 | semidirect |
| 38. C23×C32 | C2×C4 | semidirect |
| 58. #13658 | C23 | direct (N × H) |
| 75. #2179 | C2×C23 | semidirect |
| 76. #2177 | C2×C23 | semidirect |
| 77. #1426 | C2×C23 | semidirect |
| 78. #1419 | C2×C23 | semidirect |
| 79. #1418 | C2×C23 | semidirect |
| 80. #1398 | C2×C23 | semidirect |
| 95. SD64 | C4×C23 | semidirect |
| 96. D32 | C4×C23 | semidirect |
| 112. Q32 | C2×C4×C23 | semidirect |
| 116. D16 | C2×C4×C23 | semidirect |
| 125. C32 | C2×C4×C23 | semidirect |
| 126. C23 | #13658 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2263 | 2 |
| C23×#2179 | 2 |
| C23×#2177 | 2 |
| C23×#1426 | 2 |
| C23×#1419 | 2 |
| C23×#1418 | 2 |
| C23×#1398 | 2 |
| #13658 | 23 |